# Mozzi-Chasles Theorem

1. Apr 28, 2014

### fog37

Hello Forum,

I would like to discuss it with the forum if ok.

Rotation is a subtle concept and there are a lot of misconceptions. For instance, many believe that if an object is launched up in the air, the object would rotate about the center of mass....not so....

Thanks,
fog37

2. Apr 29, 2014

### UltrafastPED

Usually we answer questions; the discussion then follows, as required.

So if your questions are mathematical, use the math forum; if they are physical, this is a good place.

3. Apr 30, 2014

### fog37

Thanks UltrafastPED.

This theorem from kinematics states that the instantaneous axis of rotation for a general 3D motion of a rigid body is not passing through the center of mass. This instantaneous axis of rotation is can change from instant to instant but is unique for that specific time t.

I think it is incorrect to think that an object launched up in the air, that is rotating, spinning, is actually rotating about the center of mass. What do you think?
I believe it is wrong.

We can take a rigid body from one configuration to the next one in an infinite numbers of way (translation+rotation about any arbitrary point), correct? But that is just geometry and it has nothing to do with the actual rigid body motion, correct?

The center of mass is a very useful point. Kinetic energy can be decomposed into two terms by using the center of mass. But that does not mean that a body in the air, only under the influence of gravity, is spinning about the center of mass.

Best,
fog37

4. Apr 30, 2014