Inertia sentence example

inertia
  • The new A, B, C are called the principal moments of inertia at 0.
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  • The directions of these axes are determined by the property (24), and therefore coincide with those of the principal axes of inertia at 0, as already defined in connection with the theory of plane quadratic moments.
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  • They both protested against the political and ecclesiastical inertia of their native state, and adopted the doctrines of freedom and reason.
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  • provided the inertia of the snrin~ itself be neglected.
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  • Consequently the inertia to overcome in moving the cylinder r=b, solid or liquid, is its own inertia, increased by the inertia of liquid (a2+b2)/(a2,..b2) times the volume of the cylinder r=b; this total inertia is called the effective inertia of the cylinder r =b, at the instant the two cylinders are concentric.
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  • Denoting the effective inertia of the liquid parallel to Ox by aW' the momentum aW'U = 4)0W' (24) _ U i -AO' 25) in this way the air drag was calculated by Green for an ellipsoida pendulum.
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  • The moment of inertia about any radius of the quadric (39) therefore varies inversely as the square of the length of this radius.
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  • /n be the perpendicular distances from any given axis, the sum ~(mp2) is the quadratic moment with respect to the axis; it is also called the moment of inertia about the axis.
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  • is x+y2+z(Xx+uy+vz), the moment of inertia about this axis is =AX2+Bu+Cv12F~w2Gv?.2HXu, (37) provided A=~m(y+z)), B=~{m(z1+x)j, C=~m(x+y)}, ~ ~ 8 F=~(myz), G=~(mzx), H=~(mxy); 5 ~
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  • The graphical methods of determining the moment of inertia of a plane system of particles with respect to any line in its plane may be briefly noticed.
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  • 2 V I - a /al ' Y' I-a /al ' and the effective inertia of the liquid in the interspace Ao+2A1 W, =1 a13 +2a3W'.
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  • The point G determined by (I) is called the mass-centre or centre of inertia of the given system.
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  • In the absence of a medium the inertia of the body to transtion is the same in all directions, and is measured by the (3) But the change of the resultant momentum F of the medium as.
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  • Eschenhagen 2 first designed a set of magnetographs in which this idea of small moment of inertia was carried to its useful limit, the magnets only weighing 1 .
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  • mathematical points endowed with inertia coefficients, separated by finite intervals, and acting on one another with forces in the lines joining them subject to the law of equality of action and reaction.
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  • To find the relations between the moments of inertia about different axes through any assigned point 0, we take 0 as origin.
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  • A, B, C are the moments of inertia about the co-ordinate axes, and F, G, H are the products of inertia with respect to the pairs of co-ordinate planes.
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  • In that year, though the Church was under no direct threat of attack, owing to the inertia of the emperor Philip the Arabian, the atmosphere was full of conflict.
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  • But the presence of the medium makes the effective inertia depend on the direction of motion with respect to the external shape of the body, and on W' the weight of fluid medium displaced.
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  • The advantages of using small magnets, so that their moment of inertia may be small and hence they may be able to respond to rapid changes in the earth's field, were first insisted upon by E.
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  • With #=o, the stream is parallel to xo, and 4)=m ch (n-a)cos = - Uc ch (n-a) sh n cos /sh (n-a) (22) over the cylinder n, and as in (12) § 29, =-Ux =-Uc ch n cos t, (23) for liquid filling the cylinder; and _ th n (14) 01 th (7 7 - a) ' over the surface of n; so that parallel to Ox, the effective inertia of the cylinder n, displacing M' liquid, is increased by M'thn/th(n-a), reducing when a= oo to /If' th n = M' (b/a).
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  • It is to be remembered that all force is of the nature of a push or a pull, and that according to the accepted terminology of modern mechanics such phrases as force of inertia, accelerating force, moving force, once classical, are proscribed.
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  • The fact that the moment of inertia of the magnet varies witli the temperature must, however, be taken into account.
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  • the moment of inertia of the body about the axis, denoted by But if is the moment of inertia of the body about a mean diameter, and w the angular velocity about it generated by an impluse couple M, and M' is the couple required to set the surrounding medium in motion, supposed of effective radius of gyration k', If the shot is spinning about its axis with angular velocity p, and is precessing steadily at a rate about a line parallel to the resultant momentum F at an angle 0, the velocity of the vector of angular momentum, as in the case of a top, is C i pµ sin 0- C2µ 2 sin 0 cos 0; (4) and equating this to the impressed couple (multiplied by g), that is, to gN = (c 1 -c 2)c2u 2 tan 0, (5) and dividing out sin 0, which equated to zero would imply perfect centring, we obtain C21 2 cos 0- (c 2 -c 1)c2u 2 sec 0 =o.
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  • It appears from (24) that through any assigned point 0 three rectangular axes can be drawn such that the product of inertia with respect to each pair of co-ordinate planes vanishes; these are called the principal axes of inertia at 0.
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  • d/dI.(Mu) =X; it shows that I measures the inertia of the body as regards rotation, just as M measures its inertia as regards translation.
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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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  • Another type of quadratic moment is supplied by the deviationmoments, or products of inertia of a distribution of matter.
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  • w, or 1w, if I denote the moment of inertia (~ II) about the axis.
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  • Then the deviation y= DE of the neutral axis of the bent beam at any point D from the axis OX is given by the relation d 2 y Ml dx 2 = EI' where M is the bending moment and I the amount of inertia of the beam at D, and E is the coefficient of elasticity.
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  • Since the quadratic moments with respect to w and of are equal, it follows that w is a plane 01 stationary quadratic moment at P, and therefore a principal plane of inertia at P. In other words, the principal axes 01 inertia at P are the normals to the three confocals of the systen (3,~) which pass through P. Moreover if x, y, z be the co-ordinates of P, (33) is an equation to find the corresponding values of 0; and if Of, 02, 03 be the roots we find Oi+O2+81r1a2$-7, (35)
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  • same is true of physical quantities such as potential, temperature, &c., throughout small regions in which their variations are continuous; and also, without restriction of dimensions, of moments of inertia, &c. Hence, in addition to its geometrical applications to surfaces of the second order, the theory of quadric functions of position is of fundamental importance in physics.
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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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  • When Montanus proposed to summon all true Christians to Pepuza, in order to live a holy life and prepare for the day of the Lord, there was nothing whatever to prevent the execution of his plan except the inertia and lukewarmness of Christendom.
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  • If by the attachment of another body of known moment of inertia I, the period is altered from T to -r, we have T=21r,/l(I+I)(K~.
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  • Even with the particles retarding the motion of the aether, the same will be true if, to counterbalance the increased inertia, suitable forces are caused to act on the aether at all points where the inertia is altered.
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  • = constant, _ ff 00 NdA N BA-AA X - JA (a' +X) (b 2 +A)P - abc' a2 -b2 ' and at the surface A = o, I I N Bo-A 0 N I R - (a2+b2) abc a 2 -b 2 abc a2b2 I /b 2 N = R I /b2 - I /a2 abc I 1 I Bo - AO' a 2 b 2 - a2 b2 a 2 b2 = R (a 2 - b 2) /(a 22 + /b2) 2 - r (B o - Ao) U Bo+Co - B I - CI' Since - Ux is the velocity function for the liquid W' filling the ellipsoid A = o, and moving bodily with it, the effective inertia of the liquid in the interspace is Ao+B1+C1 Bo+Co - B1 - C, If the ellipsoid is of revolution, with b=c, - 2 XBo - - C BI' and the Stokes' current function 4, can be written down (I) is (5) (7) (6) The velocity function of the liquid inside the ellipsoid A=o due to the same angular velocity will be = Rxy (a2 - b2)/(a2 + b2), (7) and on the surface outside _ N Bo -Ao c1)0xy abc 2 62' so that the ratio of the exterior and interior value of at the surface is ?o= Bo-Ao (9) 4)1 (a 2 -6 2)/(a2 + b) - (Bo - Ao)' and this is the ratio of the effective angular inertia of the liquid, outside and inside the ellipsoid X = o.
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  • It is usually accurate enough in deflection calculations to take for I the moment of inertia at the centre of the beam and to consider it constant for the length of the beam.
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  • Consider, for example, a submarine boat under water; the inertia is different for axial and broadside motion, and may be represented by (1) c 1 =W+W'a, c2=W+W'/3' where a, R are numerical factors depending on the external shape; and if the C.G is moving with velocity V at an angle 4) with the axis, so that the axial and broadside component of velocity is u = V cos 0, v =V sin 4), the total momentum F of the medium, represented by the vector OF at an angle 0 with the axis, will have components, expressed in sec. Ib, F cos 0 =c 1 - = (W +W'a) V cos 43, F sin 0 = c 2.11 = (W +W'/3) V sin 4) .
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  • When the atoms are in motion these strain-forms produce straining and unstraining in the aether as they pass across it, which in its motional or kinetic aspect constitutes the resulting magnetic field; as the strains are slight the coefficient of ultimate inertia here involved must be great.
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  • Thus the sum ~(m.yz) is called the product of inertia with respect to the planes y=o, z=o.
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  • This may be expressed in terms of the product of inertia with respect to parallel planes through G by means of the formula (14); viz.:
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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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  • On the other hand, under the influence of the mechanics of his day, which had hardly distinguished between inertia, or the inability of a body to change itself, and resistance or the ability of bodies to oppose one another, he concluded that, as inertia is passive, so is resistance, and refused to recognize that in collision the mutual resistance of moving bodies is a force, or active power, of changing their movements in opposite directions.
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  • But on the modern theory, which includes the play of electrical phenomena as a function of the aether, there are other considerations which show that this number io 2 is really an enormous overestimate; and it is not impossible that the co-efficient of ultimate inertia of the aether is greater than the co-efficient of inertia (of different kind) of any existing material substance.
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  • The most important conception in kinetics is that of inertia.
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  • The inertia of the mass of the flying creature enables it to control and direct its movements in the air.
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  • institutional inertia is now likely to be extremely high.
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  • Polar Moment of Inertia The resistance of an object to rotational acceleration.
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  • armature coils and a commutator, its inertia is small, allowing rapid acceleration and deceleration.
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  • Bill gave COAST lots of advice on how to tackle government & bureaucratic inertia, which we will now use.
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  • negligible in terms of their effect on action inertia.
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  • The heavier the caravan the higher the yaw moment of inertia, thus the critical driving speed reduces !
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  • A desire to gain control over the inertia of life leads hummingbird-lovers to the tattoo parlor.
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  • These doctrines of inertia, and of the composite character of curvilinear motion, were scarcely apprehended even by Kepler or Galileo; but they follow naturally from the geometrical analysis of Descartes.
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  • von Bezold; the consequence was that within a few days of his arrival in Berlin in October 1878 he was able to plunge into original research on a problem of electric inertia.
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  • The numerous adjustments required by the tapper and the inertia of the apparatus prompted inventors to seek for a self-restoring coherer which should not need tapping.
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  • We may illustrate the matter as follows: A heavy pendulum possesses inertia and the property of being displaced from a position of rest but tending to return to it.
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  • Mental operations are identified with physical movements, the three conditions of physical movement, inertia, attraction and repulsion, being in the moral world self-love, love and hate.
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  • But Jerome proved quite inadequate to his position, listening to the complaints of his subordinates as to want of supplies and even of pay; he spent four whole days in absolute inertia, notwithstanding the emperor's reprimands.
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  • If A is the moment of inertia of the magnet, and t the time of a complete vibration, MH = 41r 2 A/t 2 (torsion being neglected).
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  • Wladislaus was the personification of helpless inertia.
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  • The introduction ctf the lamina (supposed to be devoid of inertia) will make no difference to the propagation of plane parallel sonorous waves through the position which it occupies.
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  • tons, (4) w denoting the density of water in tons/ft.', and W =wV, for a displacement of V ft.3 This couple, combined with the original buoyancy W through B, is equivalent to the new buoyancy through B, so that W.BB 1 =wAk 2 tan 8, (5) BM =BB 1 cot B=Ak e /V, (6) giving the radius of curvature BM of the curve of buoyancy B, in terms of the displacement V, and Ak e the moment of inertia of the water-line area about an axis through F, perpendicular to the plane of displacement.
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  • In particular, when a = oo, the extra inertia is M'.
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  • Similarly, parallel to Oy, the increase of effective inertia is NT'/th n th(n-a), reducing to M'/th n=M' (a/b), when a= oo, and the liquid extends to infinity.
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  • Similarly, the inertia parallel to Oy and Oz is NW' - 1 B W', B C (b2 +-X, c 2 ab and A +C abc/ZP, Ao For a sphere a=b=c, Ao= Bo=Co =, 'a' = Q = = z, (9) U from (II), (16) so that the effective inertia of a sphere is increased by half the weight of liquid displaced; and in frictionless air or liquid the sphere, of weight W, will describe a parabola with vertical acceleration W - W', g (30) W+ aW Thus a spherical air bubble, in which W/W' is insensible, will begin to rise in water with acceleration 2g.
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  • Single needles are never used, two being the least number, and these so arranged that the moment of inertia about every diameter of the card shall be the same.
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  • ~(m.PN1)=Iw2, (4) where I is the moment of inertia about the instantaneous axis.
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  • With the same notation for moments and products of inertia as in II (38), we have and therefore by (1),
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  • ,j If the co-ordinate axes be taken to coincide with the principal axes of inertia at 0, at the instant under consideration, we have the simpler formulae 2T=Api+Bqi+Cri, (8)
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  • In this case the kinetic energy is given by 2T = M0 (u1 +v2+w1) +AP2 +Bq2 +Cr2 2Fqr 2Grp 2Hpq, (13) where M0 is the mass, and A, B, C, F, G, H are the moments and products of inertia with respect to the mass-centre; cf.
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  • The resulting Z+R equations are not as a rule easy of application, owing to the fact that the moments and products of inertia A, B, C, F, G, H are not constants but vary in conse- 0 quence of the changing orientation of the body with respect to the co-ordinate axes.
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  • Cji=L, Cq=M, Ct=N, (18) where C is the constant moment of inertia about any axis through the mass-centre.
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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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  • The components of angular momentum about the axis of the flywheel and about the vertical will be Cn and A ~ respectively, where A is the moment of inertia about any axis through the masscentre (or through the fixed point 0) perpendicular to that of symmetry.
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  • Hence if the principal moments of inertia ~, ~
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  • In order that the moments and products of inertia with respect to these axes may be constant, it is in general necessary to suppose them fixed in the solid.
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  • If we now apply them to the case of a rigid body moving about a fixed point 0, and make Ox, Oy, Oz coincide with the principal axes of inertia at 0, we have X, u, v=Ap, Bq, Cr, whence A (B C) qr = L,
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  • If OA, OB, OC be principal axes of inertia of a solid, and if A, B, C denote the corresponding moments of inertia, the kinetic energy is given by 2TA(~ sin 4,sin 0 cos 44~)2+B Ce cos 4,+sin0 sin$)i +C (~+cos0~)2.
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  • The coefficients arr, a,~, are called the coefficients of inertia; they are not in general constants, being functions of the qs and so variable with the configuration.
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  • We may further treat the coefficients of inertia 0,-r~ a~ of 22 (I) as constants.
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  • We may note further that when ~ is small the displacement q has the equilibrium value Q/c, the same as would be produced by a steady force equal to the instantaneous value of the actual force, the inertia of the system being inoperative.
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  • Actual Energy of Circular TranslationMoment of inertia.
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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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  • 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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  • 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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  • i25.* To find the moment of inertia of a body about an axis through 1?s ceetre of gravity experimentally.Suspenc~ the body from any conveniently selected axis 0 (fig.
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  • The position of G can be found experimentally~ hence OG is known and the quantity Rican be calculated from which and the ascertained weight W of the body the moment ~f inertia about an axis through G, namely, W/gXRi, can be computed.
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  • W and I being respectively the weight and the moment of inertia of the link about the axis through the Centre of gravity.
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  • Its momen4 of inertia about G can be found experimentally by the method explained in 125, and then the value of the couple M can be computed.
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  • Dalby (London, 1906), where the inertia stresses brought upon the several links of a Joy valve gear, belonging to an express passenger engine of the Lancashire & Yorkshire railway, are investigated for an engine-speed of 68 m.
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  • Klein, New Constructions of the Force of Inertia of Connecting Rods and Couplers and Constructions of the Pressures on their Pins, Journ.
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  • Varley had advanced tentatively the hypothesis that it consisted in an actual projection of electrified matter from the cathode, and Crookes was led by his researches in 1870, 1871 and 1872 to embrace and confirm this hypothesis in a modified form and announce the existence of a fourth state of matter, which he called radiant matter, demonstrating by many beautiful and convincing experiments that there was an actual projection of material substance of some kind possessing inertia from the surface of the cathode.
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  • The final outcome of these investigations was the hypothesis that Thomson's corpuscles or particles composing the cathode discharge in a high vacuum tube must be looked upon as the ultimate constituent of what we call negative electricity; in other words, they are atoms of negative electricity, possessing, however, inertia, and these negative electrons are components at any rate of the chemical atom.
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  • No one has yet been able to isolate positive electrons, or to give a complete demonstration that the whole inertia of matter is only electric inertia due to what may be called the inductance of the electrons.
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  • Atoms of matter are composed of congeries of electrons and the inertia of matter is probably therefore only the inertia of the electromagnetic medium.'
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  • The joint operation of superficial tension and inertia in fixing the wave-length of maximum instability was first considered by Lord Rayleigh in a paper (Math.
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  • Weisbach also shows that if Gy 2 is the moment of inertia of the beam, the time, t, of a vibration of the balance is 2 (P+Q) (I' a 2) G y2 t = r gt2 (P+Q) a+Gs) This shows that the time of a vibration increases as P, Q and / increase, and as a and s diminish.
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  • If the centre of gravity of a pulley is on the axis of rotation, and the whole mass is distributed so that the axis of inertia coincides with the axis of rotation, there can be no unbalanced force or unbalanced couple as the pulley revolves.
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  • Ignorance regarding the inertia of matter drove him to this expedient.
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  • The first law of motion - that which expresses the principle of inertia - is virtually contained in the idea of uniformly accelerated velocity.
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  • Discarding these obscure and misleading notions, Galileo taught that gravity and levity are relative terms, and that all bodies are heavy, even those which, like the air, are invisible; that motion is the result of force, instantaneous or continuous; that weight is a continuous force, attracting towards the centre of the earth; that, in a vacuum, all bodies would fall with equal velocities; that the "inertia of matter" implies the continuance of motion, as well as the permanence of rest; and;:that the substance of the heavenly bodies is equally "corruptible" with that of the earth.
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  • The grand historic backcloth ends up highlighting the central weakness of the novel: the inertia of the protagonist.
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  • The third attachment point takes a single diagonal fixed belt or inertia reel extension but not a harness with straps over both shoulders.
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  • This is due to friction, inertia and other blah.
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  • The goad is an elephant goad, used to produce movement from inertia.
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  • The parameters of the rotor Hamiltonian are the three principal moments of inertia.
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  • inertia of the body.
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  • Throughout the early 1930s the Labor left constantly tried to overcome the inertia of the trade union leaders.
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  • One way to improve turbo lag is to reduce the inertia of the rotating parts, mainly by reducing their weight.
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  • increasing the inertia or lowering the torsional stiffness results in a lower resonant frequency.
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  • Make Training Evaluation Work is a book designed to break through this organizational inertia.
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  • For example, poor thermal inertia could be due to a poorly packed frost layer.
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  • This added weight creates more rotational inertia, which in turn enables the disk to spin with more constant torque.
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  • The reason is simple: financial and productivity benefits do not outweigh organizational inertia.
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  • inertia reel belt or fixed harness with two shoulder straps.
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  • Lap belt, inertia reel belt or fixed harness with two shoulder straps.
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  • inertia load is on a primary cylinder.
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  • inertia block system will win few prizes.
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  • inertia forces.
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  • inertia effects which are significant at high loading rates.
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  • Braking response and feel are outstanding, and a very lightweight, six-spoke cast aluminum wheel reduces unsprung weight and steering inertia.
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  • They had also spent several hours each day practicing the maths test used to quantify sleep inertia.
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  • Ian Mullen, BBA Chief Executive, said: " The current complex pensions ' structure fuels customer inertia.
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  • Britain's workers demand the right to smoke-free workplaces: government inertia hits two year mark.
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  • using lanyards or inertia reel devices for fall arrest on lighting trusses is still an issue.
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  • moment of inertia of the given solid about the z -axis.
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  • However the inertia of the coil reduces high frequency response.
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  • rosarydepiction implies passive inertia on the part of the congregation who heard this message, rosaries in hand.
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  • There is little that is new, much that is simply repeated and re-hashed, and only sheer inertia has kept me plowing through.
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  • turbo lag is to reduce the inertia of the rotating parts, mainly by reducing their weight.
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  • yaw moment of inertia, thus the critical driving speed reduces!
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  • According to our hypothesis, the foreign matter may be supposed to load the aether, so as to increase its inertia without altering its resistance to distortion.
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  • It has a very large starting torque, which enables it to overcome the inertia of getting the load into motion, and it lifts heavy loads at a slower speed and lighter loads at a quicker one, behaving, under the action of the controller in a somewhat similar manner to that in which the cylinders of the steam crane respond to the action of the stop-valve.
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  • 2A 0 - 2AI 2 a 1 3 - a3 When the spheres are not concentric, an expression for the effective inertia can be found by the method of images (W.
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  • If the two materials are disposed symmetrically, the amount of load carried by each would be in direct proportion to the coefficient of elasticity and inversely as the moment of inertia of the cross section.
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  • The observations are difficult, and the inertia of the instrument is liable to cause error, but much care was taken.
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  • When the frame of this arrangement is rapidly displaced through a small horizontal range to the right and left of the direction in which the rod points, the weight b by its inertia tends to remain at rest, and the motion of the frame, which is that of the earth, is magnified in the ration op to bp. This apparatus, of which there are many types, was first introduced into seismometry by Professor Ewing.
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  • (28) Let us now take as co-ordinate axes the principal axes of inertia at the mass-centre G.
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  • If A = B = C, the momental ellipsoid becomes a sphere; all axes through 0 are then principal axes, and the moment of inertia is the same for each.
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  • This gives the acceleration of m as modified by the inertia of the wheel.
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  • The depiction implies passive inertia on the part of the congregation who heard this message, rosaries in hand.
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  • Instead of overcoming a bewailed inertia, Reich 's theories hardly sufficed to sustain a ridiculous private racket.
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  • Craftsman 34118: Considered the best budget electric chainsaw, the Craftsman offers tool-free tension adjustment, automatic chain oiling, 100 feet of electric cord, and an inertia chain brake.
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  • Starpulse has a good collection of video game pictures, including all the latest games like Fatal Inertia and Castlevania: Portrait of Ruin.
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  • unless the axis of rotation be a principal axis of inertia (ii) at 0.
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  • The origin of the name deviation moment sometimes applied to a product of inertia is also now apparent.
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  • The components of linear momentum are then M~, Mi, and the angular momentum relative to G as base is JO, where M is the mass and I the moment of inertia about G.
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