How Does Angular Momentum Affect a Skater's Spin?

[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 = http://library.thinkquest.org/16600/advanced/5-7.gif.[/URL] Angular velocity is [PLAIN]http://hyperphysics.phy-astr.gsu.edu/hbase/imgmec/avel3.gif.[/URL] Knowing this, how can I derive the the new angular velocity?

 

[radou]

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

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

 

[mikefitz]

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

w=25.27 rad/s!

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^2I 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?