Equations of motion for angular acceleration

[jono90one]

Homework Statement

A slope angled 36* to the horizontal has a hoop cylindrical shell going down it, which has radius 3cm and mass 100g.
1) Write down an equation of motion for the angular acceleration.
2) Will the linear acceleration change if the hoop is changed to a cylinder (i.e. solid).

Homework Equations

I=mr^2
F=ma
T=Iα (alpha)(T=Torque)

The Attempt at a Solution

1. (Im not sure about this one, any tip would be appreciated)
Logically angular acceleration equations of motion must follow a similar structure to linear acceleration equation of motion.
i.e. Iα = ∑T
But I am not sure what torque's are acting if so?

2. The linear acceleration is easy, that is just ma = ∑F, i get
sin(x)(gcos(x)+g) = 10.4 ms^-2 (Masses cancle)

But it wants to find out if it changes,
This one I'm also not sure on, I know α(angular accel) changes, as the moment of inertia changes. But I am not sure if this changes the linear acceleration as the center of mass remains the same...

Any advice is greatly appreciated :)

 

[Delphi51]

I hesitate to post because I don't see how to do this in the way you started. I think it can be done from an energy approach. If you write that
potential energy at the top = kinetic energy at the bottom
for some distance s along the hill, and have linear KE as well as rotational KE on the right side, you need only differentiate with respect to time to get a nice formula for the acceleration. It will have the moment of inertia in it (unless you put in I = mR² for the ring) so you can see the effect of changing to a solid ring. I used w = v/r in the rotational energy expression to avoid having two variables for the velocity.