Inertia of a rolling dumbell

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SUMMARY

The moment of inertia of a rolling dumbbell, consisting of two plates of equal mass on a rod, is not affected by the distance "R" between the plates as long as the mass of the rod remains constant and the dumbbell rolls in a straight line. The only scenario where the distance would influence the moment of inertia is if the dumbbell rotates about an axis that is not parallel to the rod. This conclusion is based on the principles of rotational dynamics and the definition of moment of inertia.

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yunica
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TL;DR
How does the distance by which two plates are placed from a dumbell's center affect inertia
Hi guys,
I was just wondering this question: say I have a dumbell which is two plates of equal mass placed on a rod, then is the moment of inertia for this object affected when the distance the plates are placed from the center "R" changes?

I've attached an image to illustrate me point
1748650947950.webp


Thanks guys
 
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Welcome to PF.
yunica said:
... is the moment of inertia for this object affected when the distance the plates are placed from the center "R" changes?
No.
If the mass of the bar is constant, and it rolls in a straight line, then the separation of the weights will not determine the inertia.
 
Unless it is rotating about an axis that is not parallel to the rod
 
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