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

Consider the situation shown below we have shown the frictional forces .

(b) `F'= F=F` where F and F are external forces through support
`implies F_("net")=0 ("one each cylinder")`
External torque `=Fxx3R` (anti- clockwise )

( c) Let `omega _(1)` and `omega_(2)` be final angular velocites of samaller and bigger drum respectively (anti - clokwise and clockwise Respectivelty)
Hence , `Romega_(2)implies(omega_(1))/(omega_(2))=2`
Note :- We should be very careful while indicating direction of frictional forces.