Question

A figure skater spinning at 3.4 rad/sec with a moment of inertia of 3.2 kgm2 puts his arms out so that his new moment of inertia is 4.5 kgm2. What is his new angular speed?

Answer 1

Consider conservation of angular momentum you get:
Ang. Mom. (before)=Ang. Mom (after)
Where Ang. Mom. `=L=I*omega`
Where:
`I=` moment of inertia
`omega=` angular speed
So:
`3.2*3.4=4.5*omega_(aft)`
`omega_(aft)=2.4 (rad)/(sec)`
The skater slows down his rotaton by opening his arms.