Question

Two cylinders having radii $2R$ and $R$ and moment of inertia $4I$ and $I$ about their central axes are supported by axles perpendicular to their planes. The large cylinder is initially rotating clockwise with angular velocity ${\omega }_0$. The small cylinder is moved to the right until it touches the large cylinder and is caused to rotate by the frictional force between the two. Eventually slipping ceases and the two cylinders rotate at constant rates in opposite direction. During this

• A. angular momentum of system is conserved
• B. kinetic energy is conserved
• C. neither the angular momentum not the kinetic energy is conserved
• D. both the angular momentum and kinetic energy are conserved

Answer 1

Answer: (C)

neither the angular momentum not the kinetic energy is conserved

There is a finite net torque about point O, O' and A. Thus angular momentum is not conserved.

Initial K.E, $E_i=\frac{1}{2}\left(4I\right)w_o^2=2I{w}_o^2$

Final K.E, $E_f=\frac{1}{2}I{w}_o^2+\frac{1}{2}\left(4I\right)\frac{w_o^2}{4}=I{w}_o^2$

Thus K.E is also not conserved.