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

(1)
(ii) F' = F=F('') where F and F'' and external forces through support, External torque `=F xx 3 R`, anti-clockwise,
(ii) Let `omega_(1)` and `omega_(2)` be final angular velocities (anti-clockwise and clockwise respectively),
Finally there will be no friction, Hence, `Romega_(1) = 2Romega_(2) rArr omega_(1)/omega_(2)=2`