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Old Jun 9th 2010, 01:40 PM   #1
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lump disk mass to a point

hello

imagine a disk rotating by an axis that passes through the center of the disk

how can we find the analogue of a mass rotating by an axis?

I mean, how can we lump the whole mass of the wheel to a point?

how much will be the distance of this point from the axis?

for example to rotate a disk with radius 10 and mass 100 you need the same force as to rotate a point of mass 100 and rotation radius = ??

I suppose the radius will be some less than 10 (since not all parts of the disk are at this radius), but how much exactly?

thanks

PS: we need to do this in order to calculate other things, eg angular acceleration, etc
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Old Jun 10th 2010, 06:59 AM   #2
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Just as force = mass x linear accln,
torque = moment of inertia x angular accln

The Moment of inertia of a disk = 0.5 MR^2 and that of a rod with a point mass is MR^2 . Equate the two by adjusting the eqns to give what you want ;same torque? or same angular accln?
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Old Jun 10th 2010, 12:57 PM   #3
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Originally Posted by physicsquest View Post
Just as force = mass x linear accln,
torque = moment of inertia x angular accln

The Moment of inertia of a disk = 0.5 MR^2 and that of a rod with a point mass is MR^2 . Equate the two by adjusting the eqns to give what you want ;same torque? or same angular accln?
same torque
thanks
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