What is the relationship between torque and frictional force in this system?

[Joe Armas]

Homework Statement

In the picture

Homework Equations

Torque = I * Alpha

Alpha = a / r
Fnet = m*a

The Attempt at a Solution

I provided my work in the pictures. I figured out that the frictional force in system B is greater than in system A. I am not sure how to compare this with the frictional force from system C. I figured out the sum if the frictional forces of A and B are equal to mg sin theta, but don't know how the two compare.

 

[TSny]

Answers to (a) and (b) look good to me. According to (b), objects B and C have the same net force. Look at your free body diagrams for objects B and C. If you add the forces in the diagram for B do you get the same net force as the diagram for C?

What should be the direction of the friction force on C to make it rotate in the right direction for rolling down the plane?

 

[Joe Armas]

Answers to (a) and (b) look good to me. According to (b), objects B and C have the same net force. Look at your free body diagrams for objects B and C. If you add the forces in the diagram for B do you get the same net force as the diagram for C?

What should be the direction of the friction force on C to make it rotate in the right direction for rolling down the plane?

So Friction force on C is pointing up the ramp and its magnitude is equal to friction force on B? The frictional force on C is kinetic not static correct?

 

[TSny]

So Friction force on C is pointing up the ramp and its magnitude is equal to friction force on B?

Yes, that's the only way F_net,B can equal F_net,C.

The frictional force on C is kinetic not static correct?

To answer this, remember that the statement of the problem says that C rolls without slipping.