# Linear and Angular momentum of a rolling object

1. Jun 14, 2013

### hihiip201

Hi all:

I have been wondering:

picture a cylinder sitting above a sheet of sand paper, assume static friction between the sheet of paper and the cylinder.

if i start pulling the sheet of paper at velocity v along a direction of rolling (to the left), the moment caused by static friction of the sheet would cause a moment in clockwise direction, causing the a angular momentum C.W. But at the same time, since this force is directed in the left, there should be a linear momentum cause the this cylinder to roll to the left.

so my question is , wouldn't this imply a contradiction?
since if the cylinder is to roll to the left, there should be a C.C.W rotation?

thank you

2. Jun 14, 2013

### CWatters

3. Jun 14, 2013

### hihiip201

4. Jun 14, 2013

### rcgldr

Since the linear and angular acceleration can't be infinite, then in the case of only static friction, the sand paper (or the conveyor belt in the linked thread), would have to start off at zero velocity and then accelerate to some specific speed.

5. Jun 14, 2013

### hihiip201

Hi:

Sorry about my stupidity, I just realize that you can have the cylinder moving to the left with velocity lower than v, and rolling to the right, i thought it implied a contradiction because i forgot that we are on a moving sandpaper, not stationary. I didn't see realize that rolling only means that surface velocity must be the same as the sandpaper and the object must move to the right relative to the sand paper, so as long as it doesn't move as fast as v this would be satisfied.

thanks!

Last edited: Jun 14, 2013