Force of Friction in rolling motion without knowing r

[snoworskate]

Homework Statement

A hollow spherical shell with mass 1.50 kg rolls without slipping down a slope that makes an angle of 39.0^\circ with the horizontal.

a) Find the magnitude of the acceleration a_cm of the center of mass of the spherical shell.
b) Find the magnitude of the frictional force acting on the spherical shell.

Homework Equations

a(center of mass) = gsin(theta)/(1 +c) where c is a constant for I, here it is 2/3

Torque net = I(alpha) where alpha is angular acceleration

The Attempt at a Solution

I used the first equation in a to get the acceleration as 3.70 m/s^2. I really don't know how to do b without knowing R. I know (or think I know) that at the point of contact the frictional force must equal the torque so that the point doesn't actually move. The hint in the problem says,

"set up the corresponding Newtonian equations for the translational and rotational motions of the shell. Since there is no slipping, use both equations together to calculate the acceleration by solving the angular motion equation for the translational acceleration in terms of the frictional force, and then substituting into the translational motion equation."

I don't understand the hint. Solving for net force the force of Friction f should equal torque which equals I(alpha). Then alpha = f/I. I just don't know where to go with that. Specifically, how do I solve the "angular motion equation for the translational acceleration in terms of the frictional force"?

Thanks so much in advance! I appreciate it!

 

[ehild]

When a body is rolling (its contact point with the ground is in rest) the acceleration of the CM is equal to the angular acceleration times the radius,
a=\alpha R

The friction is force, not torque. What is the torque of the frictional force?

Write out the equation for torque , and substitute alpha by a/R. ehild

 

[snoworskate]

Perfect, thank you so much! I somehow missed that equation