Torque and energy conservation of a yoyo

[scavok]

In 1993, a giant yo-yo of mass 480 kg and measuring about 1.9 m in radius was dropped from a crane 57 m high. Assuming that the axle of the yo-yo had a radius of r=0.1 m, find the velocity of the descent v at the end of the fall.

I know that .5mv²+.5Iw²=mgh, but I don't have a clue how to find w (the angular velocity).

I really don't even know where to start. The only thing I can think of is the force due to gravity creating a torque, which would allow me to solve for the angular acceleration, but even then I would need the amount of time it takes to travel 57m in order to get the angular velocity.

If someone could point me in the right direction I would appreciate it.

 

[Euclid]

It is easy to show that $$\frac{dz}{dt}=v=R\frac{d\theta}{dt}=R\omega$$.
(To show this, simply draw a diagram - If the yo-yo rotates through an angle $$d\theta$$ what is the consequent change in z?)

 

[scavok]

Wouldn't I need the angular velocity, velocity, or time to do anything with that?

 

[Euclid]

Wouldn't I need the angular velocity, velocity, or time to do anything with that?

According to my last post, $$v = R\omega$$. This relation doesn't involve time. Try putting this into your energy conservation equation.