Two cylindrical hollow drums of radii R and 2R, and of a common height h, are rotating with angular velocities ω (anti-clockwise) and ω (clockwise), respectively. Their axes, fixed are parallel and in a horizontal plane separated by (3 R + δ). They are now brought in contact (δ → 0).

Question

Two cylindrical hollow drums of radii R and 2R, and of a common height h, are rotating with angular velocities ω (anti-clockwise) and ω (clockwise), respectively. Their axes, fixed are parallel and in a horizontal plane separated by (3 R + δ). They are now brought in contact (δ → 0).
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?

Philoid · Accepted Answer

Here F and F’ are external forces through support.

Let ω₁ and ω₂ be final angular velocities (anticlockwise and clockwise respectively)

Since there will be no friction both drum has same linear velocity.

Hence,

So,