Rotational Kinematics - Cylinder down a slope.

[CaptainSFS]

Homework Statement

A certain non-uniform but cylindrically symmetric cylinder has mass 9 kg, radius 1.2 m, and moment of inertia about the center of mass 7.6 kg m2. It rolls without slipping down a rough 20° incline.

What is the acceleration of the cylinder's center-of-mass?

Homework Equations

kinematics and the rotational equivalents

The Attempt at a Solution

The hints I was given was to find/use 3 equations. I believe the equations I found are wrong. I seem to have some difficulty with kinematics, and now especially this rotational kinematics.

I found:
m*g*sin(20) - F(friction) = m*a
T(orque) = I * alpha
a = alpha * r

Any help to whether these are the useful equations, and how I may go about using these? Thx. :)

 

[Astronuc]

What is the relationship between torque on the cylinder and the frictional force at the circumference?

 

[CaptainSFS]

Are they the same?

b/c the frictional force is a force not coming out from the CM; therefore it helps it spin? I believe it is the only other force, so they must be the same?

 

[CaptainSFS]

I also tried using the gravitational force as the Torque.
I used m*g*sin(20)=I*alpha
m*g*sin(20)/I=alpha and alpha*R = a
so... m*g*sin(20)*R/I=a,
but this didn't work either.

-------------------
I just solved this problem.

 

[llamaworm]

Use these equations:
mgsin(20) - F(friction) = ma
I(alpha) = F(friction)*r
a=(alpha)*r

The only force that applies a torque is friction, because the normal force and gravity both act on the center of mass.