Question

On average, both arms and hands together account for 13% of a person's mass, while the head is 7.0% and the trunk and legs account for 80%. We can model a spinning skater with her arms outstretched as a vertical cylinder (head, trunk, and legs) with two solid uniform rods (arms and hands) extended horizontally. Suppose a 75.0 kg skater is 1.60 m tall, has arms that are each 66.0 cm long (including the hands), and a trunk that can be modeled as being 33.0 cm in diameter. If the skater is initially spinning at 79.0 rpm with her arms outstretched, what will her angular velocity ?2 be (in rpm ) after she pulls in her arms and they are at her sides parallel to her trunk? Assume that friction between the skater and the ice is negligble.

Answer 1

Mass of head+trunk+legs = 87% of total mass, that is

Mass of arms is = 13 % of total mass, that is

Mass of skater is

Length of arm is

Radius of trunk is

Initial angular velocity of skater when arms outstretched is

Since the net external torque on the system is zero, angular momentum is conserved.

When the arms of skater are outstretched ,

Moment of inertia of head+trunk+legs is

Moment of inertia of arms is

( each arm is considered to be a rod, moment of inertia using parallel axis theorem  )

Angular momentum of the skater when arms outstretched is

When she pulls her arms parallel to her trunk,

Moment of inertia of head+trunk+legs is is unchanged.

Moment of inertia of arms is (as the whole mass of arms is located at distance R from axis)

Angular momentum of the skater when arms pulled in is

Conserving the angular momentum of the skater before and after her arms are pulled in,