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

(b) F' = F = F'' where F and F'' and external forces through support.

Fnet = 0 External torque = F × 3R, anticlockwise.

(c) Let ω1  and ω2 be final angular velocities (anticlockwise and clockwise respectively) Finally there will be no friction.

Hence, R ω1 = 2 R ω2 ⇒ ω1/ω2 = 2

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