Question
Why is the moment of inertia of a hoop that has a mass $M$ and a radius $R$ greater than the moment of inertia of a disk that has the same mass and radius?
Step 1
Step 1: The moment of inertia, $I$, for a rotating object is given by the equation $I = \sum m r^2$, where $m$ is the mass of a small piece of the object and $r$ is the distance of this piece from the axis of rotation. Show more…
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Key Concepts
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If a solid disk and a hoop have the same mass and radius, which would have the smaller rotational inertia about its center of mass? Why?
Assertion Moment of inertia of circular ring about a given axis is more than moment of inertia of the cireular disc of same mass and same size, about the same axis. Reason The circular ring hollow so its moment of inertia is more than circular disc which is solid.
Rotational Motion
Round 2
The moment of inertia for a regular object can never be larger than $M R^{2}$, where $M$ is the mass and $R$ is the size of the object. Why is this so? (Hint: Which object has a moment of inertia of $M R^{2} ?$ )
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