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instantaneous

instantaneous

instantaneous Sentence Examples

  • With Jonathan, it had been instantaneous as well.

  • In a couple of years, I won't have so many problems searching the memories.  It'll be instantaneous, like that! he said and snapped his fingers.

  • Woman, in her wasted life, in her hurried death, here stands appealing to the society that degrades her, with a combination of eloquence and poetry, of forms of art at once instantaneous and permanent, and with great metrical energy and variety.

  • Thus he approximates to the wave theory of light, though he supposed that the transmission of light was instantaneous.

  • If the total resistance against which the train is maintained in motion with an instantaneous velocity of V feet per second is R, the rate at which energy is expended in moving the train is represented by the product RV, and this must be the rate at which energy is supplied to the train after deducting all losses due to transmission from the source of power.

  • At the same time it renders more intelligible the extreme sensitiveness of the bodywall of the Nemertines, a local and instantaneous irritation often resulting in spasmodic rupture of the animal at the point touched.

  • An instantaneous deduction from the relation w= 2 n0 is that forms of uneven orders possess only invariants of even degree in the coefficients.

  • The principle gives an instantaneous solution of the question of the ultimate optical efficienc y in the method of " mirror-reading," as commonly practised in various physical observations.

  • Mag., 1904), whose point of view offers the great advantage of affording an instantaneous explanation of the peculiarity noticed by Brewster.

  • The question has also been raised whether the action of gravitation is absolutely instantaneous.

  • The effects of a bite by a poisonous snake upon a small mammal or bird are almost instantaneous, preventing its escape; and the snake swallows its victim at its leisure, sometimes hours after it has been killed.

  • When introduced directly into a vein, the effects are instantaneous.

  • Thus, for refined purposes, it cannot be assumed with any certainty that the instantaneous scale-value of the heliometer is known, or that it is a function of the temperature.

  • In determinations of stellar or solar parallax, comparison stars, symmetrically situated with respect to the object whose parallax is sought, should be employed, in which case the instantaneous scale-value may be regarded as an unknown quantity which can be derived in the process of the computation of the results.

  • His success was instantaneous and complete.

  • But, though not destroyed, the Port Arthur squadron was paralysed by the instantaneous assertion of naval superiority.

  • It is by no means the most powerful poison known, for such an alkaloid as pseud-aconitine, which is lethal in dose of about 1/200 of a grain, is some hundreds of times more toxic, but prussic acid is by far the most rapid poison known, a single inhalation of it producing absolutely instantaneous death.

  • Instantaneous death results from taking the pure acid.

  • An overwhelming naturalism swamped the older reserves of Egyptian art, and the expression of the postures, actions and familiarities of daily life, or the instantaneous attitudes of animals, became the dernier cri of fashion.

  • They are brought about by "the rod of God," which Moses wields, the effect being instantaneous and all-embracing.

  • Where accurate differential observations or photographs involving other than instantaneous exposures have to be made, the additional condition is required that the optical axis of the telescope shall accurately and automatically follow the object under observation in spite of the apparent diurnal motion of the heavens, or in some cases even of the apparent motion of the object relative to neighbouring fixed stars.

  • There are farther inconveniences in the use of such a telescope, viz., that the image undergoes a diurnal rotation about the axis of the horizontal telescope, so that, unless the sensitive plate is also rotated by clockwork, it is impossible to obtain sharp photographs with any but instantaneous exposures.

  • The limiting position J of this centre, when the two positions are taken infinitely close to one another, is called the instantaneous centre.

  • The instantaneous centre will have a certain locus in space, and a certain locus in the lamina.

  • If, AB being held fixed, the 3 quadrilateral be slightly de formed, it is obvious that the instantaneous centre J will - be at the intersection of the - .~ straight lines AD, BC, since s the displacements of the points D, C are necessarily at right angles to AD, BC, respectively.

  • If we equate these to zero we get the co-ordinates of the instantaneous centre.

  • In any continuous motion of a solid about a fixed point 0, the limiting position of the axis of the rotation by which the body can be brought from any one of its positions to a consecutive one is called the instantaneous axis.

  • If the bar be displaced in a vertical plane so that its ends slide on the two inclines, the instantaneous centre is at the point J.

  • The instantaneous centre of CD will be at the intersection of AD, BC, and if CD be drawn parallel to CD, the lines CC, DD may be taken to represent the virtual velocities of C, D turned each through B a right angle.

  • 52, if an infinitesimal deformation is possible without removing the bar CF, the instantaneous centre of CF (when AB is fixed) will be at the intersection of AF and BC, and since CC, FF represent the virtual velocities of the points C, F, turned each through a right angle, CF must be parallel to CF.

  • In problems of impact we have to deal with cases of practically instantaneous impulse, where a very great and rapidly varying force produces an appreciable change of momentum in an exceedingly minute interval of time.

  • The whole effect is summed up in the value of the instantaneous impulse, which is the timeintegral of the force.

  • Thus if an instantaneous impulse ~ changes the velocity of a mass m from u to u we havtt mumu=f.

  • Again, if the instantaneous position of G be taken as base, the angular momentum of the absolute motion is the same as the angular momentum Of the motion relative to G.

  • coincide withthe instantaneOus positimi of G, we have ~, 5i, z=o, and the theorem follows.

  • referred to G as a moving base, are equal to the rates of change of the corresponding components of angular momentum relative to a fixed base coincident with the instantaneous position of Cr.

  • The kinematical relations above explained now lead to the conclusion that in calculating the effect of extraneous forces in an infinitely short time t we may take moments about an axis passing through the instantaneous position of G exactly as if G were fixed; moreover, the result will be the same whether in this process we employ the true velocities of the particles or merely their velocities relative to G.

  • CG2.61, by 3, since the body is turning about the line of contact (C) as instantaneous axis, and the potential energy isMgh cosO.

  • If m be the mass of a particle at P, and PN the perpendicular to the instantaneous axis, the kinetic energy T is given by 2T=2~{m(w.

  • ~(m.PN1)=Iw2, (4) where I is the moment of inertia about the instantaneous axis.

  • 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.

  • The equation of the latter, referred to its principal axes, being as in II (41), the co-ordinates of the point J where it is met by the instantaneous axis are proportional to p, q, r, and the direction-cosines of the normal at J are therefore proportional to Ap, Bq, Cr, or X, u, v.

  • The preceding formulae are sufficient for the, treatment of instantaneous impulses.

  • 77 the kinetic energy generated is ~M (ic2H- Cq2)cuf, if C be the instantaneous centre; this is seen to be equal to ~F.

  • Now T = 3/41w1, where w is the angular velocity and I is the moment of inertia about the instantaneous axis.

  • drawn in the direction of the instantaneous axis, we have I I=M4/p(~ II); hence w varies asp. The locus of J may therefore be taken as the polhode (f 18).

  • If a be the inclination of the instantaneous axis to the axis of symmetry, (3 the inclination of the latter axis to the invariable line, we have rcosfl=Cw cos a, r sin ~3 = Aw sin a, (6) whence tan ~ =~ tan a.

  • 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.

  • And a continuous force may be regarded as the limit of a succession of infinitesimal instantaneous impulses.

  • In the present case the instantaneous axis returns to its initial position in the body whenever 4 increases by 2w, i.e.

  • The case of 2BT=ri, exactly, is therefore a critical case; it may be shown that the instantaneous axis either coincides permanently with the axis of mean moment or approaches it asymptotically.

  • 36 we see that the angular velocities p, q, r of the moving lines, OA, OB, OC about their instantaneous positions are p=Osin4,sin0cos4,~,q=cos4,+sin0sin4,i~,~

  • 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.

  • The line of contact T, therefore, on the surface of the cylinder bbb, is for the instant at rest, and is the instantaneous axis FIG.

  • By reasoning similar to that of 30, it appears that OT is the instantaneous axis of rotation 01 the rolling cone.

  • 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.

  • The path of a point P in or attached to the rolling cone is a spherical epitrochoid traced on the surface of a sphere of the radius OP. From P draw PQ perpendicular to the instantaneous axis.

  • Such a complex motion is called screw-like or helical motion; for each point in the body describes a helix or screw round the axis of rotation, fixed or instantaneous as the case may ~ be.

  • The relative motion of the faces of contact of the ridges anc grooves is a rotatory slidiug or grinding motion, about the line 01 contact of the pitch-surfaces as an instantaneous axis.

  • 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.

  • 103) be rolled on the inside of the pitch-circle BB of a wheel, it appears, from 30, that the instantaneous axis of the rolling curve at any instant will T a be at the point I, where it ~ E

  • The angular velocities of the two disks and of the cross are all equal at every instant; the middle point of the cross, at A, revolves in the dotted circle described upon the line of centres C1C, as a diameter twice for each turn of the disks and cross; the instantaneous axis of rotation of the cross at any instant is at I, the point in the circle Cf C2 diametrically opposite to A.

  • The line of intersection of the planes perpendicular to the paths of the two connected points at a given instant is the instantaneous axis of the link at that instant; and the velocities of the connected points are directly as their distances from that axis.

  • To find the ratio of these velocities, produce C1T~, C2T, till they intersect in K; K is the instantaneous axis of the connecting rod, and the velocity ratio is ci :v2 ::KTi :KT2.

  • moves at right angles to the central plane of its shaft and (ork, therefore the line of intersection of the central planes of the two forks at any instant is the instantaneous axis of the cross, and the velocity ratio of the points Ff, F2 (which, as the forks are equal, is also the angular velocity ratio of the shafts) is equal to the ratio of the distances of those points from that instantaneous axis.

  • Hence the instantaneous axis of the sheave FG is in the diameter FG, at the distance FG ACBC

  • Draw BE perpendicular to CB, cutting CD produced in E, then E is the instantaneous axis of the bar ADB; and the direction of motion of A is at every instant perpendicular to EAthat is, along the straight line ACa.

  • 81.* Centrodes, Instantaneous Centres, Velocity Image, Velocity Diagram.Problems concerning the relative motion of the several parts of a kinematic chain may be considered in two ways, in addition to the way hitherto used in this article and based on the principle of 34.

  • The first is by the method of instantaneous centres, already exemplified in 63, and rolling centroids, developed by Reuleaux in connection with his method of analysis.

  • Method 1.By reference to 30 it will be seen that the motion of a cylinder rolling on a fixed cylinder is one of rotation about an instantaneous axis T, and that the velocity both as regards direction and magnitude is the same as if the rolling piece B were for the instant turning about a fixed axis coincident with the instantaneous axis.

  • If the rolling cylinder B and its path A now be assumed to receive a common plane motion, what was before the velocity of the point P becomes the velocity of P relatively to the cylinder A, since the motion of B relatively to A still takes place about the instantaneous axis T.

  • 91 or 92) may be found,by considering each fixed in turn and then tracing out the locus of the instantaneous axis.

  • The axode is hence the locus of the instantaneous axis, whilst the centrode is the locus of the instantaneous centre in any plane parallel to the plane of motion.

  • There is no restriction on the shape of these rolling axodes; they may have any shape consistent with i,olling (that is, no slipping is permitted), and the relative velocity of a point P is still found by considering it with regard to the instantaneous centre.

  • These surfaces have contact at the instantaneous axis, which is now called the instantaneous axis of the two links concerned.

  • To find the form of these surfaces corresponding to a particular pair of non-adjacent links, consider each link of the pair fixed in turn, then the locus of the instantaneous axis is the axode corresponding to the fixed link, or, considering a plane of motion only, the locus of the instantaneous centre is the ceotrode corresponding to the fixed link.

  • To find the instantaneous centre for a particular link corresponding to any given configuration of the kinematic chain, it is only necessary to know the direction of motion of any two points in the link, since lines through these points respectively at right angles to their directions of motion.

  • intersect in the instantaneous centre.

  • Again, imagin d fixed, then the instantaneous centre Obd of b with regard n d is found by producing the links c and a to intersect in Obd and the shapes of the centroids belonging respectively to thi links Ii and d can be found as before.

  • Adding the centres corresponding to these several axes to the figure, it will be seen that there are six centres in connection with the four-bar chain of which four are permanent and two are instantaneous or virtual centres; and, further, that whatever be the configuration of the chain these centres group themselves into three sets of three, each set lying on a straight line.

  • Then Ob is the velocity of the point b in magnitude and direction, and cb is the tangential velocity of B relatively to C. Moreover, whatever be the actual magnitudes of the velocities, the instantaneous velocity ratio of the points C and B is given by the ratio Oc/Ob.

  • Acceleration Image.Although it is possible to obtain the acceleration of points in a kinematic chain with one link fixed by methods which utilize the instantaneous centres of the chain, the vector method more readily lends itself to this purpose.

  • It should be understood that the instantaneous centre considered in the preceding paragraphs is available only for estimating relative velocities; it cannot be used in a similar manner for questions regarding acceleration.

  • That is to say, although the instantaneous centre is a centre of no velocity for the instant, it is not a centre of no acceleration, and in fact the centre of no acceleration is in general a quite different point.

  • Find the instantaneous can- ..- I ~

  • Let r the mechanism have a small motion; then, for the instant, the link b d is turning about its instantaneous centre Oba, and, if ~, is its -.

  • instantaneous angular velocity, the velocity ~

  • which shows that the ratio of the two forces may be found by taking moments about the instantaneous centre of the link on which they act.

  • * To find the force competent to produce the instantaneous acceleration of any link of a meclianism.In many practical problems it is necessary to know the magnitude and position of the forces acting to produce the accelerations of the several links of a mechanism.

  • But this last expression is proportional to the instantaneous power taken up in the inductive circuit, and hence the difference of the two readings of the electrometer is proportional to the mean power taken up in the circuit (Phil.

  • [The continued coexistence of various thicknesses, as evidenced by the colours in the same film, affords an instantaneous proof of this conclusion.] The phenomena of very thin liquid films deserve the most careful study, for it is in this way that we are most likely to obtain evidence by which we may test the theories of the molecular structure of liquids.

  • The readiest method of obtaining instantaneous illumination is the electric spark, but with this Magnus was not successful.

  • The actual behaviour of the colliding drops becomes apparent under instantaneous illumination, e.g.

  • The formation cannot be instantaneous, and if we could measure the tension of a surface not more than 1 1) 0 of a second old, we might expect to find it undisturbed, or nearly so, from that proper to pure water.

  • The instantaneous revulsion of public feeling was somewhat unreasonable, for Pitt's health seems now to have been beyond doubt so shattered by his hereditary malady, that he was already in old age though only fifty-eight.

  • It is claimed that Leonardo knew the direction of the stroke of the wing, as revealed by recent researches and proved by modern instantaneous photography.

  • This plane remains invariable so long as no third body acts; when it does act the position of the plane changes very slowly, continually rotating round the radius vector of the planet as an instantaneous axis of rotation.

  • 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.

  • He vehemently rejected their doctrine of justification by faith; conversion might be instantaneous, but it was only the beginning of a long and gradual process of justification.

  • This second book was an instantaneous success, and indeed marks an epoch in literary history.

  • This contact may be made to close the circuit of a suitable voltmeter, or to charge a condenser in connexion with it, and the reading of the voltmeter will therefore not be the average or effective voltage of the alternator, but the instantaneous value of the electromotive force corresponding to that instant during the phase, determined by the position of the rotating contact slip with reference to the poles of the alternator.

  • If the contact springs can be moved round the disk so as to vary the instant of contact, we can plot out the value of the observed instantaneous voltage of the machine or circuit in a wavy curve, showing the wave form of the electromotive force of the alternator.

  • The electromotive force so selected is balanced against the steady potential difference produced between a fixed and a sliding contact on a wire traversed by another steady current, and if there is any difference between this last, the potential difference, and the instantaneous potential difference balanced against it, a relay is operated and sets in action a motor which shifts the contact point along the potentiometer wire and so restores the balance.

  • With Jonathan, it had been instantaneous as well.

  • In a couple of years, I won't have so many problems searching the memories.  It'll be instantaneous, like that! he said and snapped his fingers.

  • Perhaps the war will be an instantaneous, almost bloodless, victory followed by rejoicing in the streets.

  • We now have an attraction between the atoms (instantaneous dipole - induced dipole interaction ).

  • There is an affirmation of divine fiat, or instantaneous creation.

  • These include: 1500w inverter Morco instantaneous water heater Solar controller for the 160w solar panels Battery bank.

  • A hydraulic system uses a liquid because its near incompressibility makes the action instantaneous as long as the system is full of liquid.

  • instantaneous dipole - induced dipole interaction ).

  • instantaneous water heater.

  • instantaneous snapshot during the interaction of incoming wake with gas turbine blade showing dynamically adapted mesh & turbulence kinetic energy distribution.

  • instantaneous velocity is the limiting value of the average velocity measured over a very small interval.

  • instantaneous occurrence.

  • instantaneous frequency being smoothed by a time window with a total duration of about 110 ms.

  • Seek time is virtually instantaneous to retrieve a scene from any part of the disk by many search parameters.

  • I have designed a small machine code routine which makes the transfer of two sets of graphics almost instantaneous.

  • Death, once the animal is caught, is practically instantaneous.

  • Because death was nearly instantaneous, the lungs would show no infarction.

  • A process driven control loop allows the power supply response to process variations to be near instantaneous.

  • In some cases spreadsheet update is not instantaneous, however it should not be a problem for any of these spreadsheets.

  • Grix didn't know how long the trip had taken, it had seemed instantaneous to him, but he was hungry.

  • Life is stripped down to the basics and becomes truly instantaneous.

  • The software is more robust and the device provides instantaneous LOAD.

  • Anything but instantaneous, the change would appear instantaneous in the rocks.

  • A perfect channel for allowing instantaneous ordering of airport parking was now available.

  • These include: 1500w inverter Morco instantaneous water heater Solar controller for the 160w solar panels Battery bank.

  • labourant labor travels the world and international communications are instantaneous.

  • instantaneous snapshot during the interaction of incoming wake with gas turbine blade showing dynamically adapted mesh & turbulence kinetic energy distribution.

  • But, as the angle between the positionweb and the distance-webs is a constant, the remedy is to determine that angle (always very nearly a right angle) by any independent method and employ the distance-webs as position-webs in the way described, using the position-web only to determine the instantaneous index error of the position-circle.

  • Woman, in her wasted life, in her hurried death, here stands appealing to the society that degrades her, with a combination of eloquence and poetry, of forms of art at once instantaneous and permanent, and with great metrical energy and variety.

  • Thus he approximates to the wave theory of light, though he supposed that the transmission of light was instantaneous.

  • If the total resistance against which the train is maintained in motion with an instantaneous velocity of V feet per second is R, the rate at which energy is expended in moving the train is represented by the product RV, and this must be the rate at which energy is supplied to the train after deducting all losses due to transmission from the source of power.

  • The response was instantaneous: the king of France himself, who bore on his conscience the burden of an unpunished massacre by his troops at Vitry in 1142, 4 took the crusading vow on the Christmas day of 1145.

  • At the same time it renders more intelligible the extreme sensitiveness of the bodywall of the Nemertines, a local and instantaneous irritation often resulting in spasmodic rupture of the animal at the point touched.

  • An instantaneous deduction from the relation w= 2 n0 is that forms of uneven orders possess only invariants of even degree in the coefficients.

  • The principle gives an instantaneous solution of the question of the ultimate optical efficienc y in the method of " mirror-reading," as commonly practised in various physical observations.

  • Mag., 1904), whose point of view offers the great advantage of affording an instantaneous explanation of the peculiarity noticed by Brewster.

  • The question has also been raised whether the action of gravitation is absolutely instantaneous.

  • The effects of a bite by a poisonous snake upon a small mammal or bird are almost instantaneous, preventing its escape; and the snake swallows its victim at its leisure, sometimes hours after it has been killed.

  • When introduced directly into a vein, the effects are instantaneous.

  • Thus, for refined purposes, it cannot be assumed with any certainty that the instantaneous scale-value of the heliometer is known, or that it is a function of the temperature.

  • In determinations of stellar or solar parallax, comparison stars, symmetrically situated with respect to the object whose parallax is sought, should be employed, in which case the instantaneous scale-value may be regarded as an unknown quantity which can be derived in the process of the computation of the results.

  • His success was instantaneous and complete.

  • But, though not destroyed, the Port Arthur squadron was paralysed by the instantaneous assertion of naval superiority.

  • It is by no means the most powerful poison known, for such an alkaloid as pseud-aconitine, which is lethal in dose of about 1/200 of a grain, is some hundreds of times more toxic, but prussic acid is by far the most rapid poison known, a single inhalation of it producing absolutely instantaneous death.

  • Instantaneous death results from taking the pure acid.

  • An overwhelming naturalism swamped the older reserves of Egyptian art, and the expression of the postures, actions and familiarities of daily life, or the instantaneous attitudes of animals, became the dernier cri of fashion.

  • They are brought about by "the rod of God," which Moses wields, the effect being instantaneous and all-embracing.

  • Where accurate differential observations or photographs involving other than instantaneous exposures have to be made, the additional condition is required that the optical axis of the telescope shall accurately and automatically follow the object under observation in spite of the apparent diurnal motion of the heavens, or in some cases even of the apparent motion of the object relative to neighbouring fixed stars.

  • There are farther inconveniences in the use of such a telescope, viz., that the image undergoes a diurnal rotation about the axis of the horizontal telescope, so that, unless the sensitive plate is also rotated by clockwork, it is impossible to obtain sharp photographs with any but instantaneous exposures.

  • The limiting position J of this centre, when the two positions are taken infinitely close to one another, is called the instantaneous centre.

  • The instantaneous centre will have a certain locus in space, and a certain locus in the lamina.

  • If, AB being held fixed, the 3 quadrilateral be slightly de formed, it is obvious that the instantaneous centre J will - be at the intersection of the - .~ straight lines AD, BC, since s the displacements of the points D, C are necessarily at right angles to AD, BC, respectively.

  • If we equate these to zero we get the co-ordinates of the instantaneous centre.

  • In any continuous motion of a solid about a fixed point 0, the limiting position of the axis of the rotation by which the body can be brought from any one of its positions to a consecutive one is called the instantaneous axis.

  • If the bar be displaced in a vertical plane so that its ends slide on the two inclines, the instantaneous centre is at the point J.

  • Let J be the instantaneous centre for any bar CD (fig.

  • The instantaneous centre of CD will be at the intersection of AD, BC, and if CD be drawn parallel to CD, the lines CC, DD may be taken to represent the virtual velocities of C, D turned each through B a right angle.

  • 52, if an infinitesimal deformation is possible without removing the bar CF, the instantaneous centre of CF (when AB is fixed) will be at the intersection of AF and BC, and since CC, FF represent the virtual velocities of the points C, F, turned each through a right angle, CF must be parallel to CF.

  • In problems of impact we have to deal with cases of practically instantaneous impulse, where a very great and rapidly varying force produces an appreciable change of momentum in an exceedingly minute interval of time.

  • The whole effect is summed up in the value of the instantaneous impulse, which is the timeintegral of the force.

  • Thus if an instantaneous impulse ~ changes the velocity of a mass m from u to u we havtt mumu=f.

  • Again, if the instantaneous position of G be taken as base, the angular momentum of the absolute motion is the same as the angular momentum Of the motion relative to G.

  • coincide withthe instantaneOus positimi of G, we have ~, 5i, z=o, and the theorem follows.

  • referred to G as a moving base, are equal to the rates of change of the corresponding components of angular momentum relative to a fixed base coincident with the instantaneous position of Cr.

  • The kinematical relations above explained now lead to the conclusion that in calculating the effect of extraneous forces in an infinitely short time t we may take moments about an axis passing through the instantaneous position of G exactly as if G were fixed; moreover, the result will be the same whether in this process we employ the true velocities of the particles or merely their velocities relative to G.

  • CG2.61, by 3, since the body is turning about the line of contact (C) as instantaneous axis, and the potential energy isMgh cosO.

  • If m be the mass of a particle at P, and PN the perpendicular to the instantaneous axis, the kinetic energy T is given by 2T=2~{m(w.

  • ~(m.PN1)=Iw2, (4) where I is the moment of inertia about the instantaneous axis.

  • 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.

  • The equation of the latter, referred to its principal axes, being as in II (41), the co-ordinates of the point J where it is met by the instantaneous axis are proportional to p, q, r, and the direction-cosines of the normal at J are therefore proportional to Ap, Bq, Cr, or X, u, v.

  • The preceding formulae are sufficient for the, treatment of instantaneous impulses.

  • 77 the kinetic energy generated is ~M (ic2H- Cq2)cuf, if C be the instantaneous centre; this is seen to be equal to ~F.

  • Now T = 3/41w1, where w is the angular velocity and I is the moment of inertia about the instantaneous axis.

  • drawn in the direction of the instantaneous axis, we have I I=M4/p(~ II); hence w varies asp. The locus of J may therefore be taken as the polhode (f 18).

  • If a be the inclination of the instantaneous axis to the axis of symmetry, (3 the inclination of the latter axis to the invariable line, we have rcosfl=Cw cos a, r sin ~3 = Aw sin a, (6) whence tan ~ =~ tan a.

  • If the instantaneous axis only deviate slightly from the axis of symmetry the angles a, (3 are small, and ~ = (AC) A .fa; the instantaneous axistherefore completes its revolution in the body in the period 2,rAC

  • 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.

  • And a continuous force may be regarded as the limit of a succession of infinitesimal instantaneous impulses.

  • In the present case the instantaneous axis returns to its initial position in the body whenever 4 increases by 2w, i.e.

  • The case of 2BT=ri, exactly, is therefore a critical case; it may be shown that the instantaneous axis either coincides permanently with the axis of mean moment or approaches it asymptotically.

  • 36 we see that the angular velocities p, q, r of the moving lines, OA, OB, OC about their instantaneous positions are p=Osin4,sin0cos4,~,q=cos4,+sin0sin4,i~,~

  • 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.

  • Instantaneous Axis of a Cylinder rolling on a Cylinder.Let a cylinder bbb, whose axis of figure is B and angular velocity -y, roll on a fixed cylinder acm, whose axis of figure is A, either outside (as infig.

  • The line of contact T, therefore, on the surface of the cylinder bbb, is for the instant at rest, and is the instantaneous axis FIG.

  • Instantaneous Axis of a Cone rolling on a Cone.Let Oaa (fig.

  • By reasoning similar to that of 30, it appears that OT is the instantaneous axis of rotation 01 the rolling cone.

  • 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.

  • The path of a point P in or attached to the rolling cone is a spherical epitrochoid traced on the surface of a sphere of the radius OP. From P draw PQ perpendicular to the instantaneous axis.

  • Such a complex motion is called screw-like or helical motion; for each point in the body describes a helix or screw round the axis of rotation, fixed or instantaneous as the case may ~ be.

  • The relative motion of the faces of contact of the ridges anc grooves is a rotatory slidiug or grinding motion, about the line 01 contact of the pitch-surfaces as an instantaneous axis.

  • 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.

  • 103) be rolled on the inside of the pitch-circle BB of a wheel, it appears, from 30, that the instantaneous axis of the rolling curve at any instant will T a be at the point I, where it ~ E

  • The angular velocities of the two disks and of the cross are all equal at every instant; the middle point of the cross, at A, revolves in the dotted circle described upon the line of centres C1C, as a diameter twice for each turn of the disks and cross; the instantaneous axis of rotation of the cross at any instant is at I, the point in the circle Cf C2 diametrically opposite to A.

  • The line of intersection of the planes perpendicular to the paths of the two connected points at a given instant is the instantaneous axis of the link at that instant; and the velocities of the connected points are directly as their distances from that axis.

  • To find the ratio of these velocities, produce C1T~, C2T, till they intersect in K; K is the instantaneous axis of the connecting rod, and the velocity ratio is ci :v2 ::KTi :KT2.

  • moves at right angles to the central plane of its shaft and (ork, therefore the line of intersection of the central planes of the two forks at any instant is the instantaneous axis of the cross, and the velocity ratio of the points Ff, F2 (which, as the forks are equal, is also the angular velocity ratio of the shafts) is equal to the ratio of the distances of those points from that instantaneous axis.

  • Hence the instantaneous axis of the sheave FG is in the diameter FG, at the distance FG ACBC

  • Draw BE perpendicular to CB, cutting CD produced in E, then E is the instantaneous axis of the bar ADB; and the direction of motion of A is at every instant perpendicular to EAthat is, along the straight line ACa.

  • 81.* Centrodes, Instantaneous Centres, Velocity Image, Velocity Diagram.Problems concerning the relative motion of the several parts of a kinematic chain may be considered in two ways, in addition to the way hitherto used in this article and based on the principle of 34.

  • The first is by the method of instantaneous centres, already exemplified in 63, and rolling centroids, developed by Reuleaux in connection with his method of analysis.

  • Method 1.By reference to 30 it will be seen that the motion of a cylinder rolling on a fixed cylinder is one of rotation about an instantaneous axis T, and that the velocity both as regards direction and magnitude is the same as if the rolling piece B were for the instant turning about a fixed axis coincident with the instantaneous axis.

  • If the rolling cylinder B and its path A now be assumed to receive a common plane motion, what was before the velocity of the point P becomes the velocity of P relatively to the cylinder A, since the motion of B relatively to A still takes place about the instantaneous axis T.

  • 91 or 92) may be found,by considering each fixed in turn and then tracing out the locus of the instantaneous axis.

  • The axode is hence the locus of the instantaneous axis, whilst the centrode is the locus of the instantaneous centre in any plane parallel to the plane of motion.

  • There is no restriction on the shape of these rolling axodes; they may have any shape consistent with i,olling (that is, no slipping is permitted), and the relative velocity of a point P is still found by considering it with regard to the instantaneous centre.

  • These surfaces have contact at the instantaneous axis, which is now called the instantaneous axis of the two links concerned.

  • To find the form of these surfaces corresponding to a particular pair of non-adjacent links, consider each link of the pair fixed in turn, then the locus of the instantaneous axis is the axode corresponding to the fixed link, or, considering a plane of motion only, the locus of the instantaneous centre is the ceotrode corresponding to the fixed link.

  • To find the instantaneous centre for a particular link corresponding to any given configuration of the kinematic chain, it is only necessary to know the direction of motion of any two points in the link, since lines through these points respectively at right angles to their directions of motion.

  • intersect in the instantaneous centre.

  • Again, imagin d fixed, then the instantaneous centre Obd of b with regard n d is found by producing the links c and a to intersect in Obd and the shapes of the centroids belonging respectively to thi links Ii and d can be found as before.

  • Adding the centres corresponding to these several axes to the figure, it will be seen that there are six centres in connection with the four-bar chain of which four are permanent and two are instantaneous or virtual centres; and, further, that whatever be the configuration of the chain these centres group themselves into three sets of three, each set lying on a straight line.

  • Having obtained the set of instantaneous centres for a chain, suppose a is the fixed link of the chain and c any other link; then O,,,is the instantaneous centre of the two links and may be considered for the instant as the trace of an axis fixed to an extension of the link a about which c is turning, and thus problems of instantaneous velocity concerning the link c are solved as though the link c were merely rotating for the instant about a fixed axis coincident with the instantaneous axis.

  • Then Ob is the velocity of the point b in magnitude and direction, and cb is the tangential velocity of B relatively to C. Moreover, whatever be the actual magnitudes of the velocities, the instantaneous velocity ratio of the points C and B is given by the ratio Oc/Ob.

  • Acceleration Image.Although it is possible to obtain the acceleration of points in a kinematic chain with one link fixed by methods which utilize the instantaneous centres of the chain, the vector method more readily lends itself to this purpose.

  • It should be understood that the instantaneous centre considered in the preceding paragraphs is available only for estimating relative velocities; it cannot be used in a similar manner for questions regarding acceleration.

  • That is to say, although the instantaneous centre is a centre of no velocity for the instant, it is not a centre of no acceleration, and in fact the centre of no acceleration is in general a quite different point.

  • Find the instantaneous can- ..- I ~

  • Let r the mechanism have a small motion; then, for the instant, the link b d is turning about its instantaneous centre Oba, and, if ~, is its -.

  • instantaneous angular velocity, the velocity ~

  • which shows that the ratio of the two forces may be found by taking moments about the instantaneous centre of the link on which they act.

  • * To find the force competent to produce the instantaneous acceleration of any link of a meclianism.In many practical problems it is necessary to know the magnitude and position of the forces acting to produce the accelerations of the several links of a mechanism.

  • Let v l, v 2, v 3 be the instantaneous potentials of the two ends and middle of the circuit; let a quadrant electrometer be connected first with the quadrants to the two ends of the inductive circuit and the needle to the far end of the non-inductive circuit, and then secondly with the needle connected to one of the quadrants (see fig.

  • But this last expression is proportional to the instantaneous power taken up in the inductive circuit, and hence the difference of the two readings of the electrometer is proportional to the mean power taken up in the circuit (Phil.

  • [The continued coexistence of various thicknesses, as evidenced by the colours in the same film, affords an instantaneous proof of this conclusion.] The phenomena of very thin liquid films deserve the most careful study, for it is in this way that we are most likely to obtain evidence by which we may test the theories of the molecular structure of liquids.

  • The readiest method of obtaining instantaneous illumination is the electric spark, but with this Magnus was not successful.

  • The actual behaviour of the colliding drops becomes apparent under instantaneous illumination, e.g.

  • The formation cannot be instantaneous, and if we could measure the tension of a surface not more than 1 1) 0 of a second old, we might expect to find it undisturbed, or nearly so, from that proper to pure water.

  • The instantaneous revulsion of public feeling was somewhat unreasonable, for Pitt's health seems now to have been beyond doubt so shattered by his hereditary malady, that he was already in old age though only fifty-eight.

  • It is claimed that Leonardo knew the direction of the stroke of the wing, as revealed by recent researches and proved by modern instantaneous photography.

  • This plane remains invariable so long as no third body acts; when it does act the position of the plane changes very slowly, continually rotating round the radius vector of the planet as an instantaneous axis of rotation.

  • 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.

  • He vehemently rejected their doctrine of justification by faith; conversion might be instantaneous, but it was only the beginning of a long and gradual process of justification.

  • This second book was an instantaneous success, and indeed marks an epoch in literary history.

  • This contact may be made to close the circuit of a suitable voltmeter, or to charge a condenser in connexion with it, and the reading of the voltmeter will therefore not be the average or effective voltage of the alternator, but the instantaneous value of the electromotive force corresponding to that instant during the phase, determined by the position of the rotating contact slip with reference to the poles of the alternator.

  • If the contact springs can be moved round the disk so as to vary the instant of contact, we can plot out the value of the observed instantaneous voltage of the machine or circuit in a wavy curve, showing the wave form of the electromotive force of the alternator.

  • The electromotive force so selected is balanced against the steady potential difference produced between a fixed and a sliding contact on a wire traversed by another steady current, and if there is any difference between this last, the potential difference, and the instantaneous potential difference balanced against it, a relay is operated and sets in action a motor which shifts the contact point along the potentiometer wire and so restores the balance.

  • It is seemingly instantaneous at last.

  • Bonding with an older child won't be instantaneous.

  • You can sometimes find better pricing on marine battery chargers when you buy from online retailers, but you won't have the luxury of instantaneous customer service as you would with a physical store.

  • Credit decisions are not always instantaneous for catalogs that offer instant credit.

  • Of course, with mascara the results are pretty instantaneous, and allergic reactions are rare so there wasn't much to worry about from that standpoint.

  • In other words, the results are instantaneous!

  • Single lens reflex cameras perform well in regards to response time, with a near instantaneous response.

  • Keep in mind that the answer will not be instantaneous and in some cases they may not be able to help.

  • With digital photography, seeing the pictures is instantaneous, so there is immediate feedback about the subject rather than waiting for film to develop.

  • With smooth animation, you'd expect the controls to be instantaneous, right?

  • Sim City is self-published by Will Wright and is an instantaneous hit.

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