Aptitude Test Problems in Physics Science for Everyone by S Krotov ( PDFDrive.com )

I

Solutions 129

Solving the obtained equations, we find that the
velocity v 0 is

vR

110= R sin a—r

It can be seen that for R sin a = r (which corre-
sponds to the case when points A, B, and C lie on
the same straight line), the expression for vo be-
comes meaningless. It should also be noted that the
obtained expression describes the motion of the
bobbin to the right (when point B is above the
straight line AC and R sin a > r) as well as to
the left (when point B is below the straight line
AC and R sin a < r).
1.27. The velocities of the points of the ingot ly-
ing on a segment AB at a given instant uniformly
vary from vl at point A to v^2 at point B. Conse-

Fig. 143

quently, the velocity of point 0 (Fig. 143) at a
given instant is zero. Hence point 0 is an instan-
taneous centre of rotation. (Since the ingot is three-
dimensional, point 0 lies on the instantaneous rota-
tional axis which is perpendicular to the plane of
the figure.) Clearly, at a given instant, the velocity

v (^2) corresponds to the points of the ingot lying on
the circle of radius OA, while the velocity v 2 to
points lying on the circle of radius OB. (In a three-
dimensional ingot, the points having such veloci-
ties lie on cylindrical surfaces with radii OA and
OB respectively.)
9-0771