Mozzi-Chasles Theorem: Learn & Discuss on Forum

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The Mozzi-Chasles theorem highlights that the instantaneous axis of rotation for a rigid body in 3D motion does not necessarily pass through the center of mass. Misconceptions exist regarding the rotation of objects, particularly in the context of objects launched into the air, where it is incorrectly assumed they rotate around their center of mass. The discussion emphasizes that while the center of mass is a useful reference point for analyzing kinetic energy, it does not dictate the actual rotation of a body influenced solely by gravity. The theorem allows for various configurations of motion, combining translation and rotation about arbitrary points. Understanding these concepts is crucial for accurately interpreting kinematic behavior in rigid bodies.
fog37
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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
 
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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.
 
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
 
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