# Angular velocity on skater

1. Oct 26, 2006

### mikefitz

A skater is initially spinning at a rate of 15 rad/s with a rotational inertia of 2.78 kg·m2 when her arms are extended. What is her angular velocity after she pulls her arms in and reduces her rotational inertia to 1.65 kg·m2?

I have so much trouble with these problems because I haven't a clue where to begin. I know that rotational inertia = . Angular velocity is . Knowing this, how can I derive the the new angular velocity?

2. Oct 26, 2006

Think about the physical meaning of that situation. What is conserved?

P.S. This is probably the most typical example for the conservation of _______ ________.

3. Oct 26, 2006

### mikefitz

cool, I got it. 2.78 * 15 = 1.65w

I have one more conservation of momentum....

The rotational inertia for a diver in a pike position is about 15.5 kg m2; it is only 8.0 kg m2 in a tucked position (the figure above).

(a) If the diver gives himself an initial angular momentum of 106 kg m2/s as he jumps off the board, how many turns can he make when jumping off a 10.0-m platform in a tuck position? [Hint: Gravity exerts no torque on the person as he falls; assume he is rotating throughout the 10.0 m dive.]

So, I know that

P=106kg m^2
d=10m
I=8kg m^2

I need to find out what w is so that I can convert to revolutions per second and then figure out how many times the guy rotates before he comes in contact with the water, only I don't know how to do this without his mass or radius???