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Question
Why can all motions involving translation and rotation be treated as translation of COM and rotation about COM? for a freely roating body, why do we always take the axis to be passing from the center of mass despite the possibilty of the axis changing in case of a freely moving body? does not the axis depend on where and what force (and direction) you apply to a free body??

Answer
Hello Satwik,

When an object moves, you can describe the result as translation of COM and rotation about COM. What you say about the details of the movement is true. It may have rotated about some other point. The hands of a clock rotate about the shaft which is at one end, not at the COM. But you could describe the change from the position at 1:00 to the position at 1:24 as translation of COM and rotation about COM. You could also treat it as translation of the tip and rotation about tip. You could move the object between the start and end positions either way.

Treating a motion as translation of COM and rotation about COM does not allow you to study all details of the dynamics of the move. For example when you swing a bat, study of the torque and angular momentum would vary depending on what the axis of rotation actually is.

I hope this helps,
Steve

Physics

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Steve Johnson

Expertise

I would be delighted to help with questions up through the first year of college Physics. Particularly Electricity, Electronics and Newtonian Mechanics (motion, acceleration etc.). I decline questions on relativity and Atomic Physics. I also could discuss the Space Shuttle and space flight in general.

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I have a BS in Physics and an MS in Electrical Engineering. I am retired now. My professional career was in Electrical Engineering with considerable time spent working with accelerometers, gyroscopes and flight dynamics (Physics related topics) while working on the Space Shuttle. I gave formal classroom lessons to technical co-workers periodically over a several year period.

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BS Physics, North Dakota State University
MS Electrical Engineering, North Dakota State University

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