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

 

[PJC01]

Hello fog37,

Thank you for bringing up the Mozzi-Chasles theorem. It is indeed an important concept in kinematics, specifically in the study of rotational motion. This theorem states that the motion of a rigid body can be described as a combination of translation and rotation about a fixed axis. This is a fundamental concept in understanding the motion of objects in 3D space.

You are correct in pointing out that there are many misconceptions about rotation, especially when it comes to objects moving in a curved path. The common misconception that an object rotating in the air would rotate around its center of mass is a perfect example. The Mozzi-Chasles theorem helps to clarify this by showing that the rotation is actually a combination of translation and rotation about a fixed axis, not just rotation around the center of mass.

I think it would be beneficial to discuss this theorem further with the forum. Does anyone have any thoughts or questions about the Mozzi-Chasles theorem? It would be great to hear different perspectives and insights on this topic.