Why is the acceleration not equal to mg sin(theta) in pure rolling motion?

[Prabs3257]

Homework Statement

A uniform solid cylinder of mass M rolls without sliding down an incline plane of inclination theeta the frictional force acting on the cylinder is

Relevant Equations

General eqns

I know the ans comes out to be mgsintheeta/3 by using f=ma and the torque eqn but my question is as stated in the question the cylinder is in pure rolling hence friction should only try to oppose mgsintheeta so that the accelration does not change hence v remains equal to rw so why is the ans not mg sintheeta

 

[DEvens]

Compare the case of the cylinder rolling with friction, and the case of a non-rotating block sliding with no friction, and the third case of a block sitting on the incline with friction holding it in place.

The two block cases will have easy to calculate answers. The non-friction sliding block comes down with an acceleration of sin theta. The non-sliding block has a frictional force of sin theta.

Now the cylinder is somewhere between these two. It's rolling so it is accelerating. But some of the force is going into turning it, and some into making its center of mass move. So, as it rolls down it will not move as fast as a non-frictional block. And since it is giving away to the friction by rolling, the force of friction won't be as high as the case of the block held in place.

 

[Prabs3257]

Ohhh now i get it thanks man