Question

Two horizontal circular discs of different radii are free to rotate about their central axes. One disc is given some angular velocity and the other is stationary. Their rims are now brought in contact. There is friction between the rims. Correct statement from the following is:

• A. Force of friction between the rims will disappear when the discs rotate with same angular speed
• B. Force of friction between the rims will disappear when they have equal linear velocities
• C. Angular Momentum of the system is conserved
• D. Rotational Kinetic Energy of the system is conserved.

Answer 1

The correct option is B Force of friction between the rims will disappear when they have equal linear velocities

Initially when the discs are brought in contact, second disc starts to rotate and gain angular speed while the first disc loses some speed.

After some time, both the rims will attain the same speed. At this point, there is no relative motion between the discs and hence friction becomes zero.

Since, $v=r\omega$ and r of the discs is different, angular speeds are different.

Angular momentum of system remains constant unless there is no external torque acting on the system. Here, both the discs are fixed by a hinge. Now, considering momentum from center of one of the discs, there is external force and torque on the system due to the second hinge. Hence, angular momentum of the system is not conserved.

Since friction is a non-conservative force, work done by friction is not converted completely into kinetic energy and some energy is lost.

Hence, the correct answer is (b).