Question

The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center . When his hands and arms are brought in and wrapped around his body to execute the spin, the hands and arms can be considered a thin-walled hollow cylinder. His hands and arms have a combined mass 8.0 kg. When outstretched, they span 1.7 m; when wrapped, they form a cylinder of radius 24 cm. The moment of inertia about the rotation axis of the remainder of his body is constant and equal to 0.40 kg * m2.

If his original angular speed is 0.50 rev/s, what is his final angular speed? \omega_2 = ___ rev/s

Answer 1

Here,
Combined mass of hands and arms
Radius when outstretched arms
Radius when wrapped arms
The moment of inertia of the body is
Initial angular speed
Initial angular speed

Initial moment of inertia is given by:

Final moment of inertia is given by:

According to the law of conservation of angular momentum:

Therefore, the final angular speed is 1.3534 rev/s.