Rotational dynamics, semicircular arc

[Saitama]

Homework Statement

(see attachment)

Homework Equations

The Attempt at a Solution

Do I need to take torque about C here?

Any help is appreciated, Thanks!

 

[Simon Bridge]

Do I need to take torque about C here?

How else would you find the angular acceleration?

 

[Saitama]

How else would you find the angular acceleration?

I asked this because I am sure this would involve integrals and before doing the maths, I want to be sure if I am heading in the right direction.

 

[Simon Bridge]

If you can only think of one way to do a problem, it is worth a try: give it a go.
Everything involves an integral if you don't already know the result.

But it can help to have a think about the problem before starting:
* If $\beta=0$, what is the initial angular acceleration?
* How does the total mass vary with $\beta$?
* How does the location of the center of mass vary with $\beta$?

 

[Saitama]

If you can only think of one way to do a problem, it is worth a try: give it a go.
Everything involves an integral if you don't already know the result.

But it can help to have a think about the problem before starting:
* If $\beta=0$, what is the initial angular acceleration?
* How does the total mass vary with $\beta$?
* How does the location of the center of mass vary with $\beta$?

I have solved the problem, I had trouble because I misinterpreted the problem. It looked to me like a semicircular arc but it isn't. Thanks!

 

[haruspex]

I have solved the problem, I had trouble because I misinterpreted the problem. It looked to me like a semicircular arc but it isn't. Thanks!

Yes, it's a poor drawing. The point where those angles meet doesn't look like it's supposed to be the centre of the arc.