# Linear Velocity at Top (Rotational Kinematics)

1. Dec 3, 2007

### ddrtrinity

1. A bike is moving at X m/s. Its tires are .60 m in diameter. How fast is a point at the rim of the top of one of the wheels moving relative to the ground?

2. v = r omega, C = 2 pi r (?)

3. At first we thought he just wanted angular velocity. Then when we realized that his given velocity is for the axle, and that he wanted velocity compared to the ground. Then we thought perhaps it is the same, but this wouldn't be true since linear velocity would depend on the radius. When I looked at a figure in the textbook, it appeared that the linear velocity for the top at any one instant would be 0 m/s, no matter what the angular velocity was, since it opposes the bottom with static friction. So ultimately, we are just very confused.

2. Dec 5, 2007

### Shooting Star

v=rw, (w is omega) where v is the speed of the bike and also the axle. The topmost point has a horizontal speed v wrt the axle. So, the speed of the topmost point is 2v wrt the ground (or 2X m/s as given by you). This is only the instantaneous velo, mind you.

The instantaneous velo of the pt of contact is zero.