Quote:
|
Originally Posted by Venkatesh
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?
|
Assuming Friction exists between the two sphere surfaces, then the answer has to be BOTH (spinning and translating)
Quote:
|
Originally Posted by Venkatesh
.. as the small sphere striking it would not be providing a torque (as it is striking in line with the center of mass).
|
The frictional force of the small sphere on the large sphere is applied at the surface tangentially so that there will be a torque exerted on the large sphere.
Quote:
|
Originally Posted by Venkatesh
.. 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.
|
Yep, both ang mom. (L) and lin mom. (p) need to be conserved in a case like this where there's no outside forces or torques on the entire system. The interesting and the tough part is determining the magnitudes of the internal frictional force and resulting torque. Need to know more about the surfaces involved.
Your's truly,
Wizard of Oz
PS: Ever played with those wooden "tops" from the '50's / '60's. You play billiards lately. Those may be a good examples of this type of scenario.