# Rotational Dynamics

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 * $$\omega$$

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

Doc Al
Mentor
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.