Question

A spinning ice skater can increase his rate of rotation by bringing his arms and free leg closer to his body. How does this procedure affect the skater's angular momentum and kinetic energy?

• A. angular momentum remains the same while kinetic energy increases
• B. angular momentum remains the same while kinetic energy decreases
• C. both angular momentum and kinetic energy remains the same
• D. angular momentum increases while kinetic energy remains the same

Answer 1

Answer: (A)

The angular momentum remains conserved when no external torque acts on the body. this gives us the relation $I_1{\omega }_1=I_2{\omega }_2$. Now if mass is mainly distributed away from the axis of rotation, the rotational inertia is high and the velocity is low. When the hands and legs are brought close to the rotational axis, the rotational inertia decreases thereby increasing the skaters angular velocity as per the conservation of angular momentum. Increase in angular velocity implies increase in the kinetic energy. Thus option A is correct.