1. Rolling with Friction

3. Spinning wheel, CM not translating (Vcm=0) Spinning wheel, CM translating (Vcm >0) {rolling} Calculate v at all the points if R = 1m and  = 1 rad/sec Vp’= Vcm= Vp= +1m/s 0 -1m/s Calculate v at all the points if R = 1m and  = 1 rad/sec Vp’= Vcm= Vp= +2 m/s +1 m/s 0 m/s

4. Is this disk rolling or spinning in place?

5. Example Consider a basketball rolling down a ramp. Calculate the translational acceleration of the ball's center of mass as the ball rolls down. Find the angular acceleration as well. Assume the ball is a solid sphere. Let’s first look at the ball’s F.B.D  mg FnFn FfFf The key word here is “rolling”. Up to this point we have always dealt with objects sliding down inclined planes. The term “rolling” tells us that FRICTION is causing the object to rotate (by applying a torque to the ball).

6. Basketball: a thin hollow spherical mass  mg FnFn FfFf  mgcos  mgsin 

7. Bowling ball: a full, solid spherical mass  mg FnFn FfFf  mgcos  mgsin  Why his is this faster than the basketball?

8.  mg FnFn FfFf  How would you find the speed at the bottom of the incline? You would need to know the distance down the ramp and use a kinematic equation V f 2 = v i 2 + 2a parallel d How would you find the time to get to the bottom of the incline?

9. Spinning wheel, CM not translating (Vcm=0) Spinning wheel, CM translating (Vcm >0) {rolling} Calculate v at all the points if R = 1m and  = 1 rad/sec Vp’= Vcm= Vp= Calculate v at all the points if R = 1m and  = 1 rad/sec Vp’= Vcm= Vp=