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284_Physics ProblemsTechnical Physics

284_Physics ProblemsTechnical Physics - 286 Rotation of a...

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286 Rotation of a Rigid Object About a Fixed Axis Q10.12 The moment of inertia depends on the distribution of mass with respect to a given axis. If the axis is changed, then each bit of mass that makes up the object is a different distance from the axis. In example 10.6 in the text, the moment of inertia of a uniform rigid rod about an axis perpendicular to the rod and passing through the center of mass is derived. If you spin a pencil back and forth about this axis, you will get a feeling for its stubbornness against changing rotation. Now change the axis about which you rotate it by spinning it back and forth about the axis that goes down the middle of the graphite. Easier, isn’t it? The moment of inertia about the graphite is much smaller, as the mass of the pencil is concentrated near this axis. Q10.13 Compared to an axis through the center of mass, any other parallel axis will have larger average squared distance from the axis to the particles of which the object is composed.
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