Two cylindrical hollow drums of radii R and 2R and of a common 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 brougth in contact (deltararr0). (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?

Two cylindrical hollow drums of radii R and 2R and of a common height

1.	Two cylindrical hollow drums of radii R and 2R and of a common 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 brougth in contact (deltararr0). (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?
Answer» Solution :(a) Figure shows the situation given in the QUESTION. (B) `F_(1)=F=F_(2)` where `F_(1) and F_(2)` are EXTERNAL forces through support. `therefore F_("net")=0` (One each cylinder) External torque = `Fxx3R`, (anti-clockwise) (c ) LET `Omega_(1)andomega_(2)` be final angular velocities of smaller and bigger drum respectively. Finally, there will be no friction. Hence, `Romega_(1)=2Romega_(2)implies (omega_(1))/(omega_(2))=2`