Calculating Rotational Inertia of a Disk with Mass M and Radius R

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SUMMARY

The discussion focuses on calculating the rotational inertia of a disk with mass M and radius R when an additional block of mass m is placed at a distance a from the center. The correct formula for the total rotational inertia is derived as I = (M + m)R^2, acknowledging that the moment of inertia is additive. The original moment of inertia of the disk is given by I_disk = (1/2)MR^2, while the block's contribution is m * (a^2), assuming its volume is negligible. The total rotational inertia is thus the sum of these two components.

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kolua
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If there is a disk of mass M and radius R that is already rotating, then someone puts a block with mass m on it a meters away from the center of mass.
What is the rotational inertia then?

Is it I=(M+m)R^2?
 
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The moment of inertia is additive. The original moment of inertia of the disk should be ##\frac{1}{2}MR^2## and the block's is ##m\cdot (1m)^2## if it's small enough for us to ignore its volume. The answer should be the sum of above.
 

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