Any questions??

For Part (a), the coefficient of static friction between the sphere and the ramp is sufficiently large that the sphere does not slip as it rolls. Here *f ≠ μ*_{k}N.

For Part (b), the coefficient of friction is reduced such that slipping does occur. Here *f = μ*_{k}N.

Can you see the difference in rotational motion of the sphere between the no-slip and slipping cases?

*Four-step plan:*

**Step 1** - FBD: Draw a free body diagram of the sphere. Take care in getting the direction of the friction force on the sphere correct.

**Step 2** - Kinetics: Write down the Newton/Euler equations for the sphere. Be careful with your moment equation - it is recommended that you use a moment equation about the center of mass of the sphere.

**Step 3** - Kinematics: For Part (a), C is a no-slip point. Relate the angular acceleration of the sphere to the acceleration of G. For part (b), C is NOT a no-slip point. You cannot relate the angular acceleration back to the acceleration of G through kinematics. Instead you need to use: *f = μ*_{k}N.

**Step 4** - Solve