Venkatesh

11-24-2004, 10:01 PM

Just a few days ago I was playing with colored pencils in Physics and came up with an interesting problem. Unfortunately I have been unable to figure out a solution to this problem. Hopefully somebody here will have more insight into this.

Imagine a large sphere at rest, on a frictionless plane, free to both rotate and/or translate. Suddenly a small spinning and translating sphere strikes the large sphere on its horizontal circumference, in line with the center of mass, and then recoils, spinning the other way. Will the large sphere start translating or spinning?

I wasn't sure what would happen, as there were two ideas I had. My first idea was that the large sphere would not start spinning, but rather sliding, as the small sphere striking it would not be providing a torque (as it is striking in line with the center of mass). Also, linear momentum needs to be conserved, so the net change of 2mv of the small sphere needs a compensation from the larger one.

On the other hand, angular momentum also needs conservation. If the sphere is now spinning at -w and was originally spinning at w, it underwent a change in angular momentum of 2Iw. This change needs a compensation, namely the larger sphere starting to rotate.

So what actually happens? I can't think of any way to empirically test this problem, so I need the help of some wizard out there.

Thanks,

Imagine a large sphere at rest, on a frictionless plane, free to both rotate and/or translate. Suddenly a small spinning and translating sphere strikes the large sphere on its horizontal circumference, in line with the center of mass, and then recoils, spinning the other way. Will the large sphere start translating or spinning?

I wasn't sure what would happen, as there were two ideas I had. My first idea was that the large sphere would not start spinning, but rather sliding, as the small sphere striking it would not be providing a torque (as it is striking in line with the center of mass). Also, linear momentum needs to be conserved, so the net change of 2mv of the small sphere needs a compensation from the larger one.

On the other hand, angular momentum also needs conservation. If the sphere is now spinning at -w and was originally spinning at w, it underwent a change in angular momentum of 2Iw. This change needs a compensation, namely the larger sphere starting to rotate.

So what actually happens? I can't think of any way to empirically test this problem, so I need the help of some wizard out there.

Thanks,