Two cylindrical hollow drums of radii `R and 2R`, and of a commom height h, are rotating with angular velocities `omega` (anti-clockwise) and `omega` (clockwise), respectively. Their axes, fixed are parallel and in a horizontal plane separated by `(3R + delta)`. They are now brought in contact `(delta rarr 0)`.
(a) Show the frictional forces just after contact.
(b) Identify forces and torque external to the system just after contact.
(c ) What would be the ratio of final angular velocities when friction ceases ?

Explanation

(a) In Fig. we have shown the frictional forces on the two drums just after contact.
(b) If F' and F'' are external forces through support on the left and right drums respectively, then
`F' = F = F''`
`:. F_("net") = 0`.
At distance between the centre of two drums `= R + 2R = 3R`, therefore, external torque,
`tau = F xx 3R`, anticlockwise.
(c) Let `omega_(1)` be final angular velocity of left drum in anticlockwise direction and `omega_(2)` be final angular velocity of right drum in clockwise direction. As there will be no friction, finally.
`:. R (omega_(1)) = 2R(omega_(2)) or (omega_(1))/(omega_(2)) = (2)/(1)`