# Solving for inertia and angular speed

1. May 23, 2013

### physicsballer2

A 60kg skater begins a spin with an angular speed of 6.0 rad/s. By changing the position of her arms, the skater decreases her moment of inertia by 50%. What is the skater's final angular speed?

I(initial)ω(initial) = I(final)ω(final)

I used 60 kg as my inertia, is inertia and mass interchangeable in this example? Then I used 30kg because her inertia is 1/2 in the final inertia

60 (6.0) = 30ω

360 = 30ω

I said above but my biggest problem with this equation is it seems to simple, I did not think mass and inertia were able to be interchangeable, but there is no radius or time given so I am not sure what else I could solve for. If my answer is correct, why is inertia and mass equal in this example?

2. May 23, 2013

### Staff: Mentor

Mass and moment of inertia are not equal. You won't need any values for the moment of inertia; All that matters in the ratio of before and after she moves her arms.

Just call the initial moment of inertia I. What does that make the final moment of inertia?

3. May 23, 2013

### physicsballer2

The final moment of inertia is 1/2 the initial, so .5I

4. May 24, 2013

### Staff: Mentor

Exactly. So just plug those values into the formula and solve for ωfinal. (The "I" will cancel.)