Moments of Inertia

This lesson introduces the moment of inertia — the rotational analogue of mass. Just as mass measures resistance to linear acceleration, moment of inertia measures resistance to angular acceleration.

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1 Definition

For a system of particles, the moment of inertia about a given axis is:

$$\boxed{I = \sum m_i r_i^2}$$I=∑mi​ri2​​

where $r_i$ri​ is the perpendicular distance of the $i$i-th particle from the axis.

For a continuous body:

$$I = \int r^2\,\mathrm{d}m$$I=∫r2dm

Property	Detail
SI unit	kg m$^2$2
Always positive	Since $r^2 \ge 0$r2≥0
Depends on the axis	Different axes give different $I$I
Depends on mass distribution	Mass further from the axis contributes more

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2 Standard Results