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Physics: Problems and Solutions

Moment of inertia

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The moment of inertia (symbol I, SI unit kg·m2) of a rotating object is a measure of what angular acceleration will be produced by a given torque, and can therefore be thought of as the rotational equivalent of mass. It is defined as

\iiint \rho (r) r^2 dV

For a point mass, it is equal to the distance from the centre of rotation squared times the mass of the object, or

I = mr^2

The moment of inertia is also equal to angular momentum divided by angular velocity, or

I = \frac{L}{\omega}

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