# Prove a spinning yo-yo has angular velocity

1. Aug 17, 2010

### virgil123

1. The problem statement, all variables and given/known data
Show, by conservation of energy, that when a length, L, of string has unwound that a
yo-yo is spinnning with angular velocity

Remember the yo-yo has both linear and rotational velocity

2. Relevant equations

$$\omega$$= $$\sqrt{}$$gL/R$$^{2}$$

3. The attempt at a solution
I do not know where to start, any help would be appreciated.

2. Aug 17, 2010

### Mindscrape

The yo-yo converts it's potential energy to rotational energy. So the change in potential potential energy is how much the center of mass has dropped, and by energy conservation that equals the kinetic energy of rotation.

so you need
PE=mgh
Krot=.5 I w^2

3. Aug 19, 2010