# Center of rotation of a free rod

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1. Apr 10, 2015

### alba

Suppose we have a free rod on a frictionless surface: if we hit it on a tip it will translate and rotate around its CM.

What happens if we hit it at any other point between tip and CM? will it still rotate around CM?, if not, is it easy to find the center of rotation?

If not, are the 3 conservation laws still valid to find the angular velocity? I should say no because if the center is not at CM the rotation will be asymmetric.

Thanks a lot

2. Apr 10, 2015

### physichu

I'm not sure, but i think that the rotation center is a relative concept' just as the origien of the axe's is arbitrary.
for each point you will get a diffrent moment of innertia.

3. Apr 11, 2015

### jbriggs444

Suppose that the rod rotated around some point other than its CM. In other words, assume that a hypothetical center of rotation were translating and the rod was rotating around it. Can you describe in ordinary non-mathematical terms the path that the center of mass would be following?

If the center of mass follows such a path, would momentum be conserved?

4. Apr 12, 2015

### physichu

If i understand you correctly, the center of mass will rotate around the "center of rotation" which is a point that moves in a straight line. I think that the problem with this (legitimate) description of the system. Is that it is not an inertial reference frame.

5. Apr 13, 2015

### alba

I know the rod should always rotate around CM, but I asked becaause I fount this post on the web at SE : http://physics.stackexchange.com/qu...ct-and-start-purely-rotating-it/174171#174171 which seem to contrast with the other answer.

Can you explain what is an " instant center of rotation." ?and what does it mean that :".. a force not through the center of mass will rotate the body about a specified point."? what is the specified point, the instant center?