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

(^152) Aptitude Test Problems in Physics
and Ffr2 will rotate the smaller disc in the direc-
tion of rotation of the larger disc.
Having considered similar pairs of regions of
the smaller disc, we arrive at the conclusion that
immediately after coming in contact, the smaller
disc will be rotated in the direction of rotation of
the larger disc.
Let the angular velocity of the smaller disc at
a certain moment of time become co. The veloci-
Fig. 157
ties of the regions with the centres of mass at
points A 1 and A2 will be vi = v; = wr, where
r = O'A (^1) = O'A 2 (Fig. 157). The forces of friction
F'f f rl and F'r2 acting on these regions will be di-
rected along vectors v (^1) —v; (the relative velocity
of the point of the larger disc touching point Ai)
and v 2 — vs (the relative velocity of the point of
the larger disc touching point A 2 ). Obviously, the
torque of the couple Fir1 and Fir2 will accelerate
the smaller disc (i.e. the angular velocity of the
disc will vary) if V, = v; < B 1 B 2 /2 = Qr (see
Fig. 157; for the sake of convenience, the vectors
"pertaining" to point A 2 are translated to point A 1 ).
Thus, as long as co < 62, there exists a nonzero
frictional torque which sets the smaller disc into