Prove a spinning yo-yo has angular velocity

[virgil123]

Homework Statement

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

Homework Equations

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

The Attempt at a Solution

I do not know where to start, any help would be appreciated.

 

[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

 

[virgil123]

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

Thank You for your reply.

So am i correct in thinking mgh = 0.5 I w^2
and where the change of height = [gl/r^2], which is the angular velocity, or am I way off the mark??