## Instantaneous Sentence Examples

- 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. - 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. - 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. - 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). - 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. - The whole effect is summed up in the value of the
**instantaneous**impulse, which is the timeintegral of the force. - Coincide withthe
**instantaneOus**positimi of G, we have ~, 5i, z=o, and the theorem follows. - CG2.61, by 3, since the body is turning about the line of contact (C) as
**instantaneous**axis, and the potential energy isMgh cosO. - ~(m.PN1)=Iw2, (4) where I is the moment of inertia about the
**instantaneous**axis. - 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. - Now T = 3/41w1, where w is the angular velocity and I is the moment of inertia about the
**instantaneous**axis. - 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. - In the present case the
**instantaneous**axis returns to its initial position in the body whenever 4 increases by 2w, i.e. - 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. - 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. - 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 - 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
**instantaneous**centre will have a certain locus in space, and a certain locus in the lamina. - 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. - 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. - 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 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. - 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. **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.- 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.