Solving Rotational Dynamics of Mass M & R Rolling on Ramp at Angle θ

[zcdfhn]

A uniform solid sphere of mass M and radius R rolls, without slipping, down a ramp that makes an angle θ with the horizontal.

The question ask for me to find the force of friction between the ramp and the sphere.

My attempt at the problem was to utilize the x-component of the force of gravity of the sphere and then the friction must be greater than that component.

I also have a feeling to use final energy - initial energy = nonconservative work, but I can't seem to find a velocity, whether its linear or angular, which is necessary to find the energy.

Note: when a ball rolls without slipping, v=R * $$\omega$$

Thank you for your time.

 

[Beam me down]

This is rolling without slipping. So at the point of contact between the ball and plane is the ball moving or stationary?

 

[Doc Al]

My attempt at the problem was to utilize the x-component of the force of gravity of the sphere and then the friction must be greater than that component.

That's certainly true, but not enough. Hint: Apply Newton's 2nd law to both the translational and rotational motion and solve for the friction force.

Note: when a ball rolls without slipping, v=R * $$\omega$$

You'll definitely need that to relate the translational and rotational quantities.