Rolling Without slipping and inertias

[ruffrunnr]

I need help with this...

A hollow, thin walled cylinder and a solid sphere start from rest and roll without slipping down an inclined plane of length 3 m. The cylinder arrives at the bottom of the plane 2.4 seconds after the sphere. Determine th angle between the inclined plane and horizontal.

 

[lpfr]

Maybe there is a shorter way to do it. But for now I just tried this method:
Find the angular acceleration taking, as center of rotation the point of contact with the inclined plane. For this you must compute the torque due to the weight and the moment of inertia around the contact point.
You will need to compute this moment of inertia using the well known formula.
Once you have the angular acceleration you can compute the time as a function of the angle. Calculate the total angle to roll down the plan.
Do this for the two objects. The ratio of the two formulas gives you the ratio of two times.
Now you have the ration and the difference between the two times you can compute each one, and then derive the angle of the plan.