Acceleration of an object rollling down a incline.

[jwu]

Homework Statement

A cylinder of mass M and radius R rolls(without slipping) down an inclined plane whose incline angle with the horizontal is Θ. Determine the acceleration of the cylinder's venter of mass.(Derive the formula)

Homework Equations

I have the answer, but I just don't understand:

∑τ=Iα, use the parallel-axis theorem and a=Rα.
(Mg sin Θ)R=(1/2MR²+MR²)(a/R)
Rg sin Θ=3/2Ra
a=2/3g sinΘ

The Attempt at a Solution

Here's my question. Why do we need to use the parallel-axis theorem? isn't that the torque is just 1/2MR² ? Maybe I am confused with the concept of Torque. I don't know...Please help!

 

[rl.bhat]

When the cylinder is rolling without slipping, the relative motion of point of contact is zero.
So it acts as the axis of rotation of the center of mass. That is why you have to find the moment of inertia about this axis by using parallel-axis theorem.