Angular sentence example

angular
  • These letters are of simple, square, angular design.
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  • Dustin was lean and handsome with clear, cool blue eyes and sharp, angular features.
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  • Another curious theorem proposed by Bouilland in 1625 as a substitute for Kepler's second law is that the angular motion of the body as measured around the empty focus F' is (approximately) uniform.
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  • Given certain linear and angular measurements, the area must be so and so.
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  • A fifth element is the position of the pericentre, which may be expressed by its angular distance XFN from the ascending node.
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  • The rate at which work is done on a particular axle is measured by the product where T is the torque or turning moment exerted on the axle by the motor or mechanism applied to it for this purpose, and is the angular velocity of the axle in radians per second.
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  • The aperture and the number of bands being both fixed, the condition of blackness determines the angular magnitude of a band and of the spectrum.
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  • Two words are almost illegible, and the angular print slants in every direction.
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  • If the angular interval between the components of a double star were equal to twice that expressed in equation (15) above, the central disks of the diffraction patterns would be just in contact.
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  • Generally only one bow is clearly seen; this is known as the primary rainbow; it has an angular radius of about 410, and exhibits a fine display of the colours of the spectrum, being red on the outside and violet on the inside.
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  • With v=o, the angular velocity of the cylinder is 2w; in this way the velocity may be calculated of the propagation of ripples and waves on the surface of a vertical whirlpool in a sink.
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  • To take a reading the torsion-head is turned until an aluminium pointer attached to the coil is brought to the zero position on a small scale; the strength of the field is then proportional to the angular torsion.
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  • The velocity of a liquid particle is thus (a 2 - b 2)/(a 2 +b 2) of what it would be if the liquid was frozen and rotating bodily with the ellipse; and so the effective angular inertia of the liquid is (a 2 -b 2) 2 /(a 2 +b 2) 2 of the solid; and the effective radius of gyration, solid and liquid, is given by k 2 = 4 (a 2 2), and 4 (a 2 For the liquid in the interspace between a and n, m ch 2(0-a) sin 2E 4) 1 4Rc 2 sh 2n sin 2E (a2_ b2)I(a2+ b2) = I/th 2 (na)th 2n; (8) and the effective k 2 of the liquid is reduced to 4c 2 /th 2 (n-a)sh 2n, (9) which becomes 4c 2 /sh 2n = s (a 2 - b 2)/ab, when a =00, and the liquid surrounds the ellipse n to infinity.
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  • An angular velocity R, which gives components - Ry, Ix of velocity to a body, can be resolved into two shearing velocities, -R parallel to Ox, and R parallel to Oy; and then ik is resolved into 4'1+1'2, such that 4/ 1 -R-Rx 2 and 1//2+IRy2 is constant over the boundary.
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  • The components of velocity of the moving origin are denoted by U, V, W, and the components of angular velocity of the frame of reference by P, Q, R; and then if u, v, w denote the components of fluid velocity in space, and u', v', w' the components relative to the axes at a point (x, y, z) fixed to the frame of reference, we have u =U +u' - yR +zQ, v =V +v -zP +xR, w=W +w -xQ +yP.
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  • As an application of moving axes, consider the motion of liquid filling the ellipsoidal case 2 y 2 z2 Ti + b1 +- 2 = I; (1) and first suppose the liquid be frozen, and the ellipsoid l3 (4) (I) (6) (9) (I o) (II) (12) (14) = 2 U ¢ 2, (15) rotating about the centre with components of angular velocity, 7 7, f'; then u= - y i +z'i, v = w = -x7 7 +y (2) Now suppose the liquid to be melted, and additional components of angular velocity S21, 522, S23 communicated to the ellipsoidal case; the additional velocity communicated to the liquid will be due to a velocity-function 2224_ - S2 b c 6 a 5 x b2xy, as may be verified by considering one term at a time.
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  • The extension to the case where the liquid is bounded externally by a fixed ellipsoid X= X is made in a similar manner, by putting 4 = x y (x+ 11), (io) and the ratio of the effective angular inertia in (9) is changed to 2 (B0-A0) (B 1A1) +.a12 - a 2 +b 2 a b1c1 a -b -b12 abc (Bo-Ao)+(B1-A1) a 2 + b 2 a1 2 + b1 2 alblcl Make c= CO for confocal elliptic cylinders; and then _, 2 A? ?
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  • The partial differential coefficient of T with respect to a component of velocity, linear or angular, will be the component of momentum, linear or angular, which corresponds.
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  • The effective angular inertia of the body in the medium is now required; denote it by C 1 about the axis of the figure, and by C2 about a diameter of the mean section.
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  • Leonardo also discussed the old Aristotelian problem of the rotundity of the sun's image after passing through an angular aperture, but not so successfully as Maurolycus.
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  • The freezing surface, in this case, consists of three sheets each starting from an angular point of the surface, that is, from the freezing-point of a pure metal.
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  • Its angular points have then co-ordinates (x t Zdx, y t Zdy, z * zdz).
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  • This coefficient is sometimes called the " angular coefficient," and may be regarded as a measure of the deviations from Boyle's law, 'which may be most simply expressed at moderate pressures by formulating the variation of the angular coefficient with temperature.
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  • The value of the angular coefficient d(pv)/dp is evidently (b - c), which expresses the defect of the actual volume v from the ideal volume Re/p. Differentiating equation (17) at constant pressure to find dv/do, and observing that dcldO= - nc/O, we find by substitution in (is) the following simple expression for the cooling effect do/dp in terms of c and b, Sdo/dp= (n+I)c - b..
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  • Except in the larger nuggets, which may be more or less angular, or at times even masses of crystals, with or without associated quartz or other rock, gold is generally found bean-shaped or in some other flattened form, the smallest particles being scales of scarcely appreciable thickness, which, from their small bulk as compared with their surface, subside very slowly when suspended in water, and are therefore readily carried away by a rapid current.
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  • It is a very heterogeneous group, being fleshy-stemmed with a woody axis, the branches being angular, winged, flattened or cylindrical, and the flowers small, short-tubed, succeeded by small, round, peashaped berries.
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  • On the other hand, if the effects arose from balanced stresses set up inside the globe by the radiation, the effects on the vanes and on the case would be of the nature of action and reaction, so that the establishment of motion of the vanes in one direction would involve impulsion of the case in the opposite direction; but when the motion became steady there would no longer be any torque either on the vanes or on the case, and the latter would therefore come back to its previous position of equilibrium; finally, when the light was turned off, the decay of the motion of the vanes would involve impulsion of the case in the direction of their motion until the moment of the restoring torque arising from the suspension of the case had absorbed the angular momentum in the system.
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  • The angular displacement, 0, of the disk is made proportional to the displacement, s, of the point of application of the force by suitable driving gear.
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  • The angular velocity of the shaft is proportional to the rate of working.
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  • Q is supplied by a spring, the extensions of which are recorded on a drum driven proportionally to the angular displacement of the driving pulley; thus a work diagram is obtained.
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  • The quadrilateral, for instance, consists of two triangles, and its area is the product of half the length of one diagonal by the sum of the perpendiculars drawn to this diagonal from the other two angular points.
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  • Take any base X'X, and draw lines at right angles to this base through all the angular points of the figure.
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  • The velocity of propagation of a torsional disturbance along a wire of circular section may be found by the transfer of momentum method, remembering that we must now replace linear momentum by angular momentum.
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  • If 0 is the angle of twist, the angular velocity is d0/dt.
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  • Hence the angular momentum conveyed per second outwards is 2prra 4 Ud0/dt.
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  • Since no angular momentum goes out on the whole Z nwra 4 d0/dx -?- 2 pwra 4 Ud0/dt = o.
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  • This result must follow in any frame, the members of which are so connected that the joints offer little or no resistance to change in the relative angular position of the members.
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  • Lord Kelvin was thereby induced to identify magnetic force with rotation, involving, therefore, angular momentum in the aether.
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  • Long previously Lord Kelvin himself came nearer this view, in offering the opinion that magnetism consisted, in some way, in the angular momentum of the material molecules, of which the energy of irregular translations constitutes.
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  • This value of is the tangent elevation (T.E); the quadrant elevation (Q.E.) is -S, where S is the angular depression of the line of sight and if 0 is h ft.
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  • The lameness of the Greeks in angular measurement would alone show that they could not derive itinerary measures from long and accurately determined distances on the earth.
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  • If 6 F and Sc are the angular deviations of these rays, then S F - Sc is called the mean dispersion of the prism.
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  • Both bear their round or ovoid male catkins at the ends of the slender terminal branchlets; the ovoid cones, either terminal or on short lateral twigs, have thick woody scales dilated at the extremity, with a broad disk depressed in the centre and usually furnished with a short spine; at the base of the scales are from three to seven ovules, which become reversed or partially so by compression, ripening into small angular seed with a narrow wing-like expansion.
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  • Thus the Roman letters E and F are liable to be confused in capital script, but not in cursive (e, f), C, G, in capitals, c, e in the cursive writing called Caroline minuscule, c, t, in the angular cursive of the 13th century and later.
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  • The Dip of the horizon at sea is the angular depression of the apparent sea horizon, or circle bounding the visible ocean, below the apparent celestial horizon as above defined.
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  • The lower jaw is characterized by its abruptly narrowed and rounded front part supporting the pair of large in cisors, as well as by the small size of the coronoid process, and the great development of the lower hind, or angular, portion.
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  • The projection at the right-hand lower corner of the figure is the angular process of the lower jaw.
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  • In the rodents now to be considered, the angular process of the lower jaw arises from the outer side of the sheath of the incisor.
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  • Within these, and forming by far the largest part of the seed, are large polygonal cells filled with very numerous and very minute angular starch grains.
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  • The telescope serves to examine the image of the slit and to measure the angular separation of the different slit images; when photographic methods are employed the telescope is replaced by a camera.
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  • When the slit is narrow light is lost through diffraction unless the angular aperture of this condensing lens, as viewed from the slit, is considerably greater than that of the collimator lens.
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  • Angular prism spectroscopes are the commonest.
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  • By suitably replacing the ocular of the observing telescope in an angular vision spectroscope by a photographic camera, it is possible to photograph spectra; such instruments are termed spectrographs.
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  • In heraldry, a bevel is an angular break in a line.
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  • The grains should show no signs of decay, and by preference should be of an angular shape.
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  • Generally speaking,broken stones will be rough and angular, whereas the stones in flint gravel will be comparatively smooth and round.
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  • These are much more liable to occur when the stones are flat and angular than when they are round.
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  • These angular;distances are attained only when the sun is on the horizon, and they increase as it rises.
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  • Immediately above this plane surface and almost touching it is a system of wires which enables angular distances from the centre of the field to be read at the eyepiece below.
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  • There has been much contirversy concerning the nature and origin of the blue ground itself; and even granted that (as is generally believed) the blue ground is a much serpentinized volcanic breccia consisting originally of an olivine-bronzite-biotite rock (the so-called kimberlite), it contains so many rounded and angular fragments of various rocks and minerals that it is difficult to say which of them may have belonged to the original rock, and whether any were formed in situ, or were brought upfrom below as inclusions.
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  • But in the " Drift " maps many other types of deposit are indicated, such, for instance, as the ordinary modern alluvium of rivers, and the older river terraces (River-drift of various ages), including gravels, brickearth and loam; old raised sea beaches and blown-sand (Aeolian-drift); the " Head " of Cornwall and Devon, an angular detritus consisting of stones with clay or loam; clay-with-flints, rainwash (landwash), scree and talus; the " Warp," a marine and estuarine silt and clay of the Humber; and also beds of peat and diatomite.
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  • In these cases the veins are often united by cross veinlets, which do not, however, form an angular network.
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  • The sheaths (Chamaerops), showing the veins ending in a process 1, called running from the base to the mara ligule; the blade of the gin, and not forming an angular leaf, f.
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  • The following data for the apparent angular width of arcs were obtained at Cape Thorsden, the arcs being grouped according to the height of the lower edge above the horizon.
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  • According to numerous observations made at Cape Thorsden, the apparent angular velocity of arcs increases on the average with their altitude.
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  • Heights have been calculated in various less direct ways, by observing for instance the angular altitude of the summit of an arc and the angular interval between its extremities, and then making some assumption such as that the portion visible to an observer may be treated as a circle whose centre lies over the so-called auroral pole.
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  • The more distant this is from the pendulum the greater is the magnification of the angular movements of the mirror.
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  • Another region, "the angular region," is similarly related to intelligent apprehension of words seen, though not of words heard.
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  • It should be noticed that clocks, on which Tycho Brahe depended very little, were used at Cassel for finding the difference of right ascension between Venus and the sun before sunset; Tycho preferred observing the angular distance between the sun and Venus when the latter was visible in the daytime.
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  • In such work the painters of Upper Germany at this time, working in the spirit of the late Gothic style just before the dawn of the Renaissance, show considerable technical attainments, with a love of quaint costumes and rich draperies crumpled in complicated angular folds, some feeling for romance in landscape backgrounds, none at all for clearness or balance in composition, and in the attitudes and expressions of their overcrowded figures a degree of grotesqueness and exaggeration amounting often to undesigned caricature.
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  • The Silurian greywackes and shales that underlie almost the whole of the Uplands weather generally into small angular debris, and at a tolerably uniform rate of disintegration.
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  • In other cases it is secured by the intersection of joints, whereby a rock, in itself hard and durable, is divided into small angular blocks, which are separated by the action of the elements and slide down the declivities.
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  • The optical apparatus generally consists of a mirror mounted on an axis parallel to the axis of the earth, and rotated with the same angular velocity as the sun.
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  • It is easily seen that if the mirror be rotated at the same angular velocity as the sun the right ascensions will remain equal throughout the day, and therefore this device reflects the rays in the direction of the earth's axis; a second fixed mirror reflects them in any other fixed direction.
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  • By adjusting the right ascension of the plane ABC and rotating the axis with the angular velocity of the sun, it follows that BC will be the direction of the solar rays throughout the day.
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  • He had angular features, a very ruddy complexion, sandy hair, and hazel-flecked, grey eyes.
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  • Further, by causing the hour circle, and with it the polar axis, to rotate by clockwork or some equivalent mechanical contrivance, at the same angular velocity as the earth on its axis, but in the opposite direction, the telescope will, apart from the effects of refraction, automatically follow a star from rising to setting.
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  • The driving circle is also much too small, so that a very slight mechanical freedom of the screw in the teeth involves a large angular freedom of the telescope in right ascension, while its position at the lower end of a too weak polar axis tends to create instability from torsion of that axis.
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  • When the angular momentum is too great for the usual spheroidal form to persist, this gives place to an ellipsoid with three unequal axes; this is succeeded by a pear-shaped form.
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  • As the simple star radiates heat and contracts, it retains its angular momentum; when this is too great for the spheroidal form to persist, the star may ultimatel y separate into two components, which are driven farther and farther apart by their mutual tides.
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  • Regarded as a linear velocity, the parallactic motion is the same for all stars, being exactly equal and opposite to the solar motion; but its amount, as measured by the corresponding angular displacement of the star, is inversely proportional to the distance of the star from the earth, and foreshortening causes it to vary as the sine of the angular distance from the apex.
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  • By this arrangement the angular rotation of the reflected beam is less than that of the magnet, and hence the spot of light reflected from this mirror yields a trace on a much smaller scale than that given by the ordinary mirror and serves to give a complete record of even the most energetic disturbance.
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  • The symbol for M has still five strokes, s has the angular form 5, 5.
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  • Leaves of aluminium foil may with advantage be substituted for gold-leaf, and a scale is sometimes added to indicate the angular divergence of the leaves.
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  • We may, for instance, employ the three Cartesian co-ordinates of a particular point 0 of the body, and three angular co-ordinates which express the orientation of the body with respect to 0.
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  • Tait that a similar representation of the type (30) is obtained if we replace the circle by an equiangular spiral described, with a constant angular velocity about the pole, in the direction of diminishing radius vector.
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  • The second general result is the Principle of Angular Momentum.
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  • If extraneous forces act, the total angular momentum about any fixed axis is in time t increased by the total extraneous impulse about that axis.
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  • If there are no extraneous forces, or if the extraneous forces have zero moment about any axis through G, the vector which represents the resultant angular momentum relative to G is constant in every respect.
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  • On this basis we can predicate the principles of linear and angular momentum, as in 15.
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  • If we integrate with respect to I between fixed limits, we obtain the principles of linear and angular momentum in the form previously given, Hence, whichever form of postulate we adopt, we are led to the principles of linear and angular momentum, which form in fact the basis of all our subsequent work.
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  • Then dU/dt, =w say, is the angular velocity of the body.
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  • The angular momentum of a particle m at a distance r from the axis is mwr.
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  • The angular velocity being constant, the effective force on a particle m at a distance r from Oz is snw2r toward& this axis, and its components are accordingly w2mx, wfmy, 0.
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  • If the extraneous forces have zero moment about G the angular velocity 0 is constant.
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  • It may also be deduced from the principles of linear and angular momentum as embodied in the equations (9).
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  • It is to be carefully noticed that the axis of resultant angular momentum about 0 does not in general coincide with the instantaneous axis of rotation.
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  • The axis of resultant angular momentum is therefore normal to the tangent plane at J, and does not coincide with OJ unless the latter be a principal axis.
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  • The motion of a rigid body in the most general case may be specified by means of the component velocities u, v, w of any point 0 of it which is taken as base, and the component angular velocities p, q, r.
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  • The circle is described with the constant angular velocity o.
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  • As an example of this latter type, suppose that a sphere is placed on the highest point of a fixed sphere and set spinning about the vertical diameter with the angular velocity n; it will appear that under a certain condition the motion of G consequent on a slight disturbance will be oscillatory.
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  • The slightest frictional forcessuch as the resistance of the aireven if they act in lines through the centre of the rolling sphere, and so do not directly affect its angular momentum, will cause the centre gradually to descend in an ever-widening spiral path.
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  • Now T = 3/41w1, where w is the angular velocity and I is the moment of inertia about the instantaneous axis.
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  • Again, the vector which represents the angular momentum with respect to 0 will be constant in every respect.
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  • The motion of the body relative to 0 is therefore completely represented if we imagine the momental ellipsoid at 0 to roll without sliding on a plane fixed in space, with an angular velocity proportional at each instant to the radius-vector of the point of contact.
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  • If p, q, r be the component angular velocities about the principal axes at 0, we have (Ap+B2q+C,2)/r = (Ap+Bq1+Cr2)/2T, (3) each side being in fact equal to unity.
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  • The angular velocity (r) about this axis is then constant.
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  • For we have seen that r is constant when there are no extraneous forces; and r is evidently not affected by an instantaneous impulse which leaves the angular momentum Cr, about the axis of symmetry, unaltered.
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  • The moving axes Ox, Oy, 01 form a rigid frame of reference whose motion at time t may be specified by the three component angular velocities p, q, r.
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  • The components of angular momentum about Ox, Qy, 01 will be denoted as usual by X, u, v.
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  • Hence the altered angular momentum about Ox will be X+OX+(is+Ou)(rOt)+ (v+Oe)qOt.
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  • As a first application of the equations (2) take the case of a solid constrained to rotate with constant angular velocity to about a fixed axis (1, m, n).
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  • The meaning of these quantities is easily recognized; thus X is the angular momentum about a horizontal axis normal to the plane of 0, u is the angular momentum about the vertical OZ, and s is the angular momentum about the axis of symmetry..
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  • Let the angular velocity of the rotation be denoted by a=dO/dt, then the linear velocity of any point A at the distance r from the axis is or; and the path of that point is a circle of the radius r described about the axis.
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  • Let -y denote the total angular velocity of the rotation of the cone B about the instantaneous axis, $ its angular velocity about the axis OB relatively to the plane AOB, and a the angular velocity with which the plane AOB turns round the axis OA.
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  • It is required to find the ratios of those angular velocities.
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  • Let V5 denote the velocity of advance at a given instant, which of course is common to all the particles of the body; a the angular velocity of the rotation at the same instant; 2,r = 6.2832 nearly, the circumference of a circle of the radius unity.
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  • In the investigation, therefore, of the comparative motion, of the driver and follower, in an elementary combination, it is unnecessary to consider relations of angular direction, which are already fixed by the connection of each piece with the frame; so that the inquiry is confined to the determination of the velocity ratio, and of tbe directional relation, so far only as it expresses the connection between forward and backward movements of the driver and follower.
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  • Application to a Pair of TurnIng Fseces.Let ai, a2 be the angular velocities of a pair of turning pieces; Of, Oi the angles which their line of connection makes with their respective planes of rotation; Ti, r2 the common perpendiculars let fall from the line of connection upon the respective axes of rotation of the pieces.
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  • That the angular velocities of a pair of turning pieces in rolling contact must be inversely as the perpendicular distances of any pair of points of contact from the respective axes.
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  • That the linear velocity of a shifting piece in rolling contact with a turning piece is equal to the product of the angular velocity of the turning piece by the perpendicular distance from its axis to a pair of points of contact.
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  • Hence, in any pair of circular wheels which work together, the numbers of teeth in a complete circumference are directly as the radii and inversely as the angular velocities.
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  • Hence also, in any pair of circular wheels which rotate continuously for one revolution or more, the ratio of the numbers of teeth and its reciprocal the angular velocity ratio must be expressible in whole numbers.
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  • The angular velocity ratio due to the sliding contact of the teeth will be the same with that due to the rolling contact of the pitch-circles, if the line of connection of the teeth cuts the Ca line of centres at the pitchpoint.
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  • Thus the relative motion of the wheels is unchanged; but I is considered as fixed, and 2 has the total motion, that is, a rotation about the instantaneous axis I, with the angular velocity cii+a1.
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  • The only modification required in the formulae is, that in equation (26) the difference of the angular velocities should be substituted for their sum.
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  • Any other convenient figure may be assumed for the path of contact, and the corresponding forms of the teeth found by determining what curves a point T, moving along the assumed path of contact, will trace on two disks rotating round the centres of the wheels with angular velocities bearing that relation to the component velocity of T along TI, which is given by Principle II.
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  • The angular velocities of the screws are inversely as their numbers of threads.
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  • Coupling of Parallel AxesOldhams CouplingA coupling is a mode of connecting a pair of shafts so that they shall rotate in the same direction with the same mean angular velocity.
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  • The angular velocities of a pair of connected circular pulleys or drums are inversely as the effective radii.
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  • The axes of rotation of a pair of turning pieces connected by a link are almost always parallel, and perpendicular to the line of connection n which case the angular velocity ratio at any instant is the recipocal of the ratio of the common perpendiculars let fall from the me of connection upon the respective axes of rotation.
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  • Coupling of Parallel Axes.Two or more parallel shafts (such as those of a locomotive engine, with two or more pairs of driving wheels) are made to rotate with constantly equal angular velocities by having equal cranks, which are maintained parallel by a coupling-rod of such a length that the line of c000exion is equal to the distance between the axes.
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  • Let ai, a2, af be the angular velocities of the first, intermediate, and last shaft in this train of two Hookes couplings.
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  • Then, from the principles of 60 it is evident that at each instant ai/ai = ai/aa, and consequently that ai; so that the fluctuations of angular velocity ratio caused by the first coupling are exactly neutralized by the second, and the first and last shafts have equal angular velocities at each instant.
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  • Required the relation between the velocity of translation 02 of W and the angular velocity af of the differential barrel.
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  • If dw/dt is the angular acceleration of the link, dw/dt X CB is the tangential acceleration of the point B about the point C. Generally this tangential acceleration is unknown in magnitude, and it becomes part of the problem to find it.
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  • The principles of this reduction are that the ratio of the given to the equivalent force is the reciprocal of the ratio of the velocities of their points of application, and the ratio of the given to the equivalent couple is the reciprocal of the ratio of the angular velocities of the pieces to which they are applied.
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  • When the relative motion of the rubbing surfaces is one of rotation, the work of friction in a unit of time, for a portion of the rubbing surfaces at a given distance from the axis of rotation, may be found by multiplying together the friction of that portion, its distance from the axis, and the angular velocity.
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  • Its moment is found by multiplying the normal pressure between the rolling surfaces by an arm, whose length depends on the nature of the rolling surfaces, and the work lost in a unit of time in overcoming it is the product of its moment by the angular velocity of the rolling surfaces relatively to each other.
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  • Neglecting the mass of the shaft itself, when the shaft rotates with an angular velocity a, the centrifugal force Wae/g will act upon the shaft and cause its axis to deflect from the axis of rotation a distance, y say.
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  • In finding the position in which the bob will revolve with a given angular velocity, a, for most practical cases connected with machinery the mass of the rod may be considered as insensible compared with that of the bob.
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  • Let a small body of the weight w undergo translation in a circulai path of the radius p, with the angular velocity of deflexion a, so that the common linear velocity of all its particles is v=ap. Then the actual energy of that body is WV2/2g = Waip2/2g.
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  • The product wp/g, by which the half-square of the angular velocity is multiplied, is called the moment of inertia of the revolving body.
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  • Flywheels.A flywheel is a rotating piece in a machine, generally shaped like a wheel (that is to say, consisting of a rim with spokes), and suited to store and restore energy by the periodical variations in its angular velocity.
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  • The principles according to which variations of angular velocity store and restore energy are the same as those of 117, only substituting moment of inertia for mass, and angular for linear velocity.
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  • The actual energy due to the rotation of the fly, with its mean angular velocity, is equal to one-half of the periodical excess of energy multiplied by the steadiness.
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  • Let da be the deviation of angular velocity to be produced in the interval dt, and I the moment of the inertia of the body about an axis through its centre of gravity; then 1/8Id(&) = Iada is the variation of the bodys actual energy.
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  • To find the angular acceleration A, draw kI, bt respectively parallel to and at right angles to the link KB.
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  • Then tb represents the angular acceleration of the point B relatively to the point K and hence tb/KB is the value of A, the angular acceleration of the link.
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  • His features were angular and somewhat harsh, but with a striking face and very fine eyes of a brilliant dark blue.
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  • Large masses of granite are found in many parts of Sweden, in Kronoberg, Orebro, Goteborg, Stockholm, &c. Sometimes the granite graduates into gneiss; sometimes (as north of Stockholm) it encloses large angular pieces of gneiss.
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  • The latter is less compact and contains angular boulders, often of a considerable size, but no powder.
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  • The irritation of the conjunctiva caused by dust leads to winking of the eyelids, lachrymation and rubbing, which tend to remove it; but after the dust has been removed violent rubbing tends rather to keep up the irritation; and sometimes, if the particle of dust remains under the eyelid and is sharp and angular, the process of rubbing may cause it to injure the conjunctiva much more than if it were left alone.
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  • They are large perennial climbers growing from short thick underground stems, from which rise numerous semi-woody flexuous angular stems, bearing large alternate stalked long-persistent and prominently net-veined leaves, from the base of which spring the tendrils which support the plant.
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  • The basement storey has the same number of faces formed into convex flutes which are alternately angular and semicircular.
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  • The next has semicircular flutes, and in the third they are all angular.
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  • The anode residue is collected in the angular bottom of the tank, the electrolyte passes from the anode chamber to a series of tanks in which the more electro-negative constituents (silver, &c.) are chemically separated, and thence to the cathode chamber, where the copper is deposited electrolytically, thence it passes again to the anode chamber and so completes the cycle.
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  • These are often wedge-shaped and angular; in some cases they consist of a short, thick stalk, terminating in a peltate expansion, or prolonged upwards in the form of a triangular lamina.
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  • A male flower consists of a single angular perianth, through the open apex of which the flower-axis projects as a slender column terminating in two anthers.
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  • The equations of surfaces of equal angular motion would be of the form r =R (i --6 cos 2 0), where e is proportional to the square of the angular motion, supposed small, and R increases as e diminishes.
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  • But this theory gives no clue to the results relating to hydrogen, which belongs to a high level, and which Adams has shown to move with an angular velocity decidedly greater than the equatorial angular velocity below it, and not to show any sign of falling off towards the poles.
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  • Lines of lanthanum and carbon which are believed to belong to a low level showed systematically smaller angular velocity than the average.
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  • Apart then from absorption there will be a discontinuous change in brightness in the apparent disk at that value of the angular radius d which corresponds to tangential emission from the upper lever r' of this mirage-forming region.
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  • The greater µ is, the greater would be the value of d, the apparent angular radius, corresponding to horizontal emission from a given level r, and that whether we accept Schmidt's theory or not.
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  • Better determinations of the actual value came from the heliometer, and gave an angular diameter of 31' 59.26" =0.10", and the value of the polar diameter exceeded the equatorial by 0.038" =0.023".
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  • The Shu-li as described by Mr Taintor are almost of the same stature as the Chinese, but have a more decided copper colour, higher cheek-bones and more angular features, while their eyes are not oblique.
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  • In a small commonplace book, bearing on the seventh page the date of January 1663/1664, there are several articles on angular sections, and the squaring of curves and " crooked lines that may be squared," several calculations about musical notes, geometrical propositions from Francis Vieta and Frans van Schooten, annotations out of Wallis's Arithmetic of Infinities, together with observations on refraction, on the grinding of " spherical optic glasses," on the errors of lenses and the method of rectifying them, and on the extraction of all kinds of roots, particularly those " in affected powers."
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  • This notation survives in reference to the minute (') and second (") of angular measurement, and has been extended, by analogy, to the foot (') and inch (").
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  • Many of the boulders are of considerable size and they are often still angular.
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  • If M is the central mass, n the angular velocity, and a the distance, the balance of the two forces is expressed by the equation an' =.1111a2, whence a 3 n 2 = M, a constant.
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  • It is an elementary principle of mechanics that this force varies directly as the product of the distance of the moving body from the centre of motion into the square of its angular velocity.
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  • When the telescope is turned in this plane, the angular motion of the line of sight is equal to that through which the circle has turned.
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  • The angular motion of the telescope in passing from this position to that when the celestial object is in the line of sight is the distance (ND) of the body from the nadir.
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  • The Kokshal-tau, which consists of several parallel ranges, is truly alpine in character and bears large glaciers, which send out polyp-like arms into U-shaped valleys, behind which the mountain peaks tower up into sharp-cut, angular " matterhorns."
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  • Then, by an obvious law of kinematics, the angular motion round the earth would be most rapid at the point nearest the earth, that is at perigee, and slowest at the point most distant from the earth, that is at apogee.
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  • Thus the apogee and perigee became two definite points of the orbit, indicated by the variations in the angular motion of the moon.
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  • It is brittle, and when hammered readily breaks up into a powder of angular grains.
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  • The object is then projected with such acute pencils on the plane focused for, in this case on the plane on which the eye can just accommodate itself, that the circle of confusion arising there is still so small that it is below the limit of angular visual distinctness and on that account appears as a sharp point.
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  • As we saw above, the apparent size of a detail of an object must be greater than the angular range of vision, i.e.
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  • In addition, the particles can only be recognized as separate objects if their apparent distance from one another is greater than the angular definition of sight.
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  • As shown in Lens and Aberration, for reproduction through a single lens with spherical surfaces, a combination of the rays is only possible for an extremely small angular aperture.
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  • The ratio of half the length of the visible piece of the scale to its distance from the diaphragm on the stage gives the tangent of half the angular aperture.
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  • The angular or numerical aperture can then be read off.
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  • The latitude of a point on the earth's surface is its angular distance from the equator, measured on the curved surface of the earth.
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  • Over the same interval Type A sequence boundaries become angular rather than parallel unconformities, suggesting increased tilting of the basin margin.
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  • The downside is that the unit looks too angular for the M20?
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  • All hi-tech, covered in glass and very angular.
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  • Early blight shows as distinctive dark brown spots, somewhat angular, with concentric rings and bounded by the leaf veins.
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  • Instead of scales, the body and tail are apparently enclosed in rows of plates, making them feel slightly angular.
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  • After the sharply angular esthetic of the exterior of the church the visitor is surprised by the curves that everywhere meet the eye inside.
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  • Most of the grains between rounded and angular, but are nearer rounded rather than angular in shape so are sub-rounded.
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  • Abstract Jones matrices describe the polarization, or spin angular momentum, of a light beam as it passes through an optical system.
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  • As a result, to conserve angular momentum, the rate of rotation must increase.
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  • Finally, if the infalling gas has too much angular momentum it cannot form circumstellar disks and all goes into a circumbinary disk.
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  • We devise an equivalent of the Jones matrix formulation for light possessing orbital angular momentum.
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  • Madabhushi, S.P.G., Schofield, A.N., Lesley, S. A new stored angular momentum (SAM) based earthquake actuator.
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  • As more pairs are broken, the nucleons contribute more single-particle spin to the total angular momentum.
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  • The large angular momentum in this massive disk leads to turbulence and increased interaction of the constituents.
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  • They can be used very generally to study the angular momentum and spectroscopic factors associated with specific single particle states.
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  • It is a coarse breccia, that is a stone in which are embedded angular stone fragments.
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  • Surface water carrying dissolved calcium carbonate has cemented these angular fragments together in many places forming a breccia.
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  • The angular integral of the reduced matrix element is expressed in terms of recoupling coefficients and coefficients of fractional parentage.
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  • Chancel arch truss distinguished by its angular wooden corbels; the roof between the trusses paneled over in wood.
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  • With his binoculars, he measures an angular deviation of 62 mile from the church to the target.
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  • The object was about the apparent size (angular diameter) of the full moon.
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  • The link lengths and the crank angular displacement are varied.
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  • The ecliptic latitude of an object in the sky is its angular distance north or south of the ecliptic latitude of an object in the sky is its angular distance north or south of the ecliptic.
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  • This transfer function is then used to calculate the distorted partial-wave matrix elements which are used to generate the angular distribution.
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  • A distinctive feature of the fabrics is a considerable number of cavities from which an angular grit has leached.
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  • I am angular in the chart and all my world class opponents are ill or injured or otherwise indisposed and I win.
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  • The angular integrals are carried out using the methods of Racah algebra.
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  • The ecliptic latitude of an object in the sky is its angular distance north or south of the ecliptic.
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  • Downstairs angular walls add a quaint quirkiness to a ground floor bedroom that is tastefully decorated in soft lilac.
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  • Also covers effect of angular misalignment on fluid film hearing performance, and includes the moments applied by the bearing itself.
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  • This angular momentum leads to a magnetic moment of fixed size for each particle.
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  • Unfortunately aluminum nitride in particular has angular particles which are abrasive, leading to excessive mold wear.
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  • We'd both gotten turned onto Gang Of Four around then so we were playing angular post punk.
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  • For the most commonly used cut of silicon crystal, this angular range is approximately 3 micro radians.
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  • The distance between the two images, and their angular separation can easily be edited using a new Stereo control panel.
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  • Look for angular black colored hard slate as these rocks can contain Trilobites from the Silurian shales.
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  • The stuff in which the gold occurred at Mount Brown was composed of broken slate with a few angular fragments of quartz.
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  • This sealed several archeologically sterile layers of coarse angular sands alternating with fine organic rich silts, possibly turf lines.
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  • However, Saturn is receiving a trine from an angular Moon which is placed in the terms of Mercury.
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  • The limestone outcrops have several locally uncommon species including rock whitebeam and angular Solomon's Seal.
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  • The above gear ratio equation can be used to calculate the angular velocity of the large gear from the small gear.
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  • He inserted a slip of metal, of variable breadth, at the focus of the telescope, and observed at what part it exactly covered the object under examination; knowing the focal length of the telescope and the width of the slip at the point observed, he thence deduced the apparent angular breadth of the object.
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  • The " tetrahedral theory " brought forward by Lowthian Green,' that the form of the earth is a spheroid based on a regular tetrahedron, is more serviceable, because it accounts for three very interesting facts of the terrestrial plan - (1) the antipodal position of continents and ocean basins; (2) the tri angular outline of the continents; and (3) the excess of sea in the southern hemisphere.
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  • Mean R anomaly is the anomaly which the body would have if it moved from the pericentre around F with a uniform angular motion such that its revolution would be completed in its actual time (see Orbit).
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  • In the ancient astronomy the anomaly was taken as the angular distance of the planet from the point of the farthest recession from the earth.
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  • At a later period the fall of angular fragments at the entrance finally closed the cave, and it ceased to be accessible except to a few burrowing animals, whose remains are found above the second and newer stalagmite floor.
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  • If we inquire what is the greatest admissible longitudinal aberration (Sf) in an object-glass according to the above rule, we find Sf =Xa 2 (2), a being the angular semi-aperture.
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  • If it were desired to use an angular aperture so large that the aberration according to (13) would be injurious, Rowland points out that on his machine there would be no difficulty in applying a remedy by making v slightly variable towards the edges.
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  • Considered by itself, with the cylinders held fixed, the vortex sets up a circumferential velocity m/r on a radius r, so that the angular momentum of a circular filament of annular cross section dA is pmdA, and of the whole vortex is pm7r(b2-a2).
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  • Any circular filament can be started from rest by the application of a circumferential impulse 7rpmdr at each end of a diameter; so that a mechanism attached to the cylinders, which can set up a uniform distributed impulse rpm across the two parts of a diameter in the liquid, will generate the vortex motion, and react on the cylinder with an impulse couple-pmira 2 and pm7rb 2, having resultant pm7r(b 2 -a 2), and this couple is infinite when b = oo, as the angular momentum of the vortex is infinite.
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  • Frahm,' during an important investigation on the torsional vibration of propeller shafts, measured the relative angular displacement of two flanges on a propeller shaft, selected as far apart as possible, by means of an electrical device (Engineering, 6th of February 1903).
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  • If BN, CP, DQ, FS, GT are the perpen diculars to AE from the angular points, the ordinates NB, PC,..
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  • Lecidea), sometimes obsolete, and which are occa sionally irregular in shape, angular or flexuose (e.g.
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  • The extension of the image away from the axis or size of field available for covering a photographic plate with fair definition is a function in the first place of the ratio between focal length and aperture, the longer focus having the greater relative or angular covering power, and in the second a function of the curvatures of the lenses, in the sense that the objective must be free from coma at the foci of oblique pencils or must fulfil the sine condition (see Aberration).
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  • Trains of Wheelwork.Let A1, A2, A3, &c., A,,,_1, A,,, denote a series of axes, and aj, a1, a3, &c., a,,,1, a,,, their angular velocities.
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  • In astronomy, the term is used in connexion with the Ptolemaic theory to denote the angular distance on the epicycle of a planet from the true apogee of the epicycle; and the "equation to the argument" is the angle subtended at the earth by the distance of a planet from the centre of the epicycle.
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  • We 'd both gotten turned onto Gang Of Four around then so we were playing angular post punk.
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  • Keywords DEGREES By default, all angular inputs and keywords are assumed to be in radian units.
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  • You can find faucets that are rounded and lack any corners, or more angular designs that stand out.
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  • If your face is angular, don't choose frames with sharp corners.
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  • If the design of your basin or bath is understated, adding bold and angular brassware will help create a modern focal point in your bathroom.
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  • Smooth, sleek lines and polished surfaces are common elements of modern style, as are geometric and angular shapes, asymmetry and neutral colors.
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  • Go with lighter colors - Vivid, bright colors may be in style, but they can make your space look tinier and more angular.
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  • Another gorgeous set of expressive eyebrows, but not just any angular model; Carolina also brings highly coveted posing skills to the modeling world.
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  • The stems are angular and the prickles stout, scattered, and sometimes a little curved.
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  • Smilax Aspera - A well-marked species, with angular and usually prickly stems, reaching a height of 5 to 10 feet.
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  • Variety mauritanica has angular stems of a considerable length and bearing few prickles; they are also rare on the leaves.
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  • Smilax Glauca - This plant has angular stems of about 3 feet, armed with rather stout numerous or scattered prickles, or may sometimes be without any.
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  • If you are tall and angular, you'll look great with striped ties.
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  • Celebrity fashion understands the glamour of big lenses on petite or angular faces.
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  • This can be achieved through wider frames that have an angular or rectangular bend.
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  • The angular shape of this style will flatter most men's faces.
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  • Angular faces will benefit from the curved sides and top of the heart shape.
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  • They work well with rounded and angular features, on males and females.
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  • The squared edges of the frame will make them look especially balanced against rounder features, though they're not so angular that those with more chiseled features could never wear them.
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  • Though lots of men go for angular shapes, here's a rounded style; these look great, too, and help balance out a very angular face.
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  • Girls with angular faces will love these.
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  • The lines are strong, angular, and the bridge is flat.
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  • People with a round face, for example, need glasses which help to elongate the face, and should look out for square or angular styles which will minimise the roundness of the face.
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  • If your face is round, look for angular frame shapes.
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  • The M style, sometimes referred to as Mambos, is very angular, with no frame attached to the bottom of the lenses.
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  • This ebony pair is extremely angular and gets excellent to very good marks for its condition.
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  • If your face is already fairly angular, you'll be best served by the traditional, more rounded aviator shape.
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  • Don't choose the deepest lenses if your face is round or small, or the shallowest lenses if your face is angular or long.
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  • Because the frames are rectangular with rounded edges, they'll flatter several different face shapes, from angular to round.
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  • Angular is generally a term used to describe young wines that display predominately sharp, bitter or tart flavor characteristics.
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  • Elements that are easily identifiable in furniture pieces are elegant, geometrical designs and angular pieces.
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  • Once hair is dry, spray some hairspray into the palm of your hair and gently sculpt the style into a modern and angular shape.
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  • Roses might look angular, realistic or even comical, depending on the instructions.
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  • Whether you have an angular or ultra curvy figure, are short or tall, clothing that is either baggy or too tight will not be flattering.
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  • This style of ring offers the elaborate beauty of a multi-stone design, but it features a more angular and geometric appearance.
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  • The only difference between a true cloud design and this backpack is that the clouds here are more angular than round and "puffy".
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  • During the winter solstice, the sun is the greatest angular distance away, resulting in the shortest day of the year.
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  • The spectacular, angular, 150,000 square foot building stands at the foot of downtown Cleveland against the scenic and ever-changing backdrop of Lake Erie.
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  • This pure, gold watch tantalizes the eye with a dainty bracelet designed in modern angular patterns.
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  • A hairstyle that flatters your friend's round face may very well look horrible on your long, angular face.
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  • This angle, therefore, divided by the magnifying power of the telescope gives the real angular distance of the centres of a double star.
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  • A ray of light from a lamp is thrown on the mirror, whence it is reflected upon a white surface or scale set at a distance of about 3 ft., forming a bright spot on the surface; the slightest angular deflexion of the mirror, owing to its distance from the scale, moves the spot of light a very appreciable distance to the right or left according to the direction of the angular movement.
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  • The blocks are angular, and rest irregularly one upon another, supported in all positions by the angles and edges of those beneath.
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  • The green and angular fruit or "nut" ripens in October; it is about 4 in.
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  • Shadows were used as indices of the sun's position, in combination with angular divisions.
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  • In astronomy the word denotes the angular distance of a body from the pericentre of the orbit in which it is moving.
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  • The instrument can be provided with a curve or table showing the current corresponding to each angular displacement of the torsion head.
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  • To do this the actual speed in the orbit, and in a yet higher degree the angular speed around F, must be greatest at pericentre, and continually diminish till the apocentre is reached.
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  • From the law of angular motion of the latter its radius vector will run ahead of PQ near A, PQ will overtake and pass it at apocentre, and the two will again coincide at pericentre when the revolution is completed.
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  • Instead of the period it is common in astronomical practice to use the mean angular speed, called the mean motion of the body.
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  • This is defined as the speed of revolution of the fictitious body already described, revolving with a uniform angular motion and the same periodic time as the planet.
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  • The angle from the pericentre to the actual radius vector, and the length of the latter being found, the angular distance of the planet from the node in the plane of the orbit is found by adding to the true anomaly the distance from the node to the pericentre.
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  • The development from the angular to the curved shape of S may be seen in its occurrences on the early cippus found in the Roman Forum in 1899.
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  • Apart from doubtful instances it is there six times clearly engraved; four of the instances are angular, the other two are more or less rounded.
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  • They vary in texture from a fine-grained compact oolite to a coarse-grained rock composed of angular or rounded fragments, and they commonly exhibit strongly marked false bedding.
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  • The larger ones polarize light, have angular outlines like those of crystals, and may even show twinning and definite optical properties by which they can be identified as belonging to felspar, augite or some other rock-forming mineral.
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  • Deflections of the suspended needle are indicated by the movement of a narrow beam of light which the mirror reflects from a lamp and focusses upon a graduated cardboard scale placed at a distance of a few feet; the angular deflection of the beam of light is, of course, twice that of the needle.
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  • Let us now consider the distribution of brightness in the image of a double line whose components are of equal strength, and at such an angular interval that the central line in the image of one coincides with the first zero of brightness in the image of the other.
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  • If the angular interval between the components of a double line be half as great again as that supposed in the figure, the brightness midway between is 1802 as against 1.0450 at the central lines of each image.
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  • Now since AP is very small, AL' - PL'= AP sin a, where a is the angular semi-aperture L'AB.
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  • If 2R be the diameter of the objectglass and D the distance of the object, the angle subtended by AP is E/D, and the angular resolving power is given by X/2 D sin a = X/2 R (3) This method of derivation (substantially due to Helmholtz) makes it obvious that there is no essential difference of principle between the two cases, although the results are conveniently stated in different forms. In the case of the telescope we have to deal with a linear measure of aperture and an angular limit of resolution, whereas in the case of the microscope the limit of resolution is linear, and it is expressed in terms of angular aperture.
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  • It is necessary that the aperture of the pupil be accommodated to the angular extent of the spectrum, or reciprocally.
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  • The mathematical discussion of Airy showed that the primary rainbow is not situated directly on the line of minimum deviation, but at a slightly greater value; this means that the true angular radius of the bow is a little less than that derived from the geometrical theory.
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  • A small sphere of the fluid, if frozen suddenly, would retain this angular velocity.
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  • Reservations must include This 1930 sans serif face has some odd angular insertions.
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  • Structure in the angular distributions is analyzed using a semiclassical optical model.
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