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The moment of inertia, or rotational inertia, determines the torque needed for a desired angular acceleration about a rotational axis. Like inertial mass is the resistance to being linearly accelerated, the moment of inertial is the resistance to being rotationally accelerated.

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How does the moment of inertia of a pendulum changes if you add a mass on the free spinning ...

The initial moment of inertia $ \frac{ML^2}{12} $ of the pendulum is about an axis/center of rotation. If you add a point object with mass $ m_{obj} $ at a distance $ r_{obj} $ from the axis/center, …
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