Question

Two horizontal disc of different radii are free to rotate about their central vertical axes. One is given some angular velocity, the other is stationary. Their rims are now brought in contact. There is friction between the rims. Then

• A. the force of friction between the rims will disappear when the disc rotate with equal angular speeds
• B. the force of friction between the rims will disappear when they have equal linear velocities
• C. the angular momentum of the system will be conserved
• D. the rotational kinetic energy of the system will not be conserved

Answer 1

Answer: (B), (D)

The correct options are
B the force of friction between the rims will disappear when they have equal linear velocities
D the rotational kinetic energy of the system will not be conserved

Initially the point A tends to slide on the rim of second disc.Thus kinetic friction force at A will act in upward direction and at B in downward direction.

This kinetic friction will act untill sliding of one point with respect to other ceases.Hence when both points have same linear velocities then $f$ will disappear.

Work-energy theorem: $W_f=\Delta K.E$

As $W_f\ne 0$ thus K.E is not conserved.

Also angular momentum of the system is not conserved.