Finding angular velocity using work energy theorem

[theBEAST]

Homework Statement

Homework Equations

Inertia about pin = ml^2/3
Work done by rotation = M*theta = 0.5(Inertia about pin) *ω²

The Attempt at a Solution

I tried two different methods and both came out to be the same answer. However they did not correspond to any of the multiple choice answers... What am I doing wrong?

Thanks!

 

[frogjg2003]

Method 1: The angular acceleration varies with $\cos(\theta)$. So using constant acceleration formulas doesn't work. You simply can't use that method.

Method 2: The potential energy is still $U=mgh$, not $U=M\theta$.

 

[theBEAST]

Method 1: The angular acceleration varies with $\cos(\theta)$. So using constant acceleration formulas doesn't work. You simply can't use that method.

Method 2: The potential energy is still $U=mgh$, not $U=M\theta$.

Thanks, but why does Mtheta not work?

 

[frogjg2003]

I'm not even sure what M is.

 

[theBEAST]

I'm not even sure what M is.

Moment about the pin.

 

[frogjg2003]

It's still wrong. It should be $\frac{1}{2}M\omega$. But that by itself contains no information about the fact it's in gravity.