Mozzi-Chasles Theorem: Learn & Discuss on Forum

[fog37]

Hello Forum,

I have recently learned about this important theorem of kinematics, the Mozzi-Chasles theorem.
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

 

[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.

 

[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.fog37

 

[UltrafastPED]

This question has been discussed in detail here:
https://www.physicsforums.com/showthread.php?t=252436
https://www.physicsforums.com/showthread.php?t=554675
https://www.physicsforums.com/showthread.php?t=697733
https://www.physicsforums.com/showthread.php?t=207229