dimensional analysis (moment of inertia)

Question

Dimensions of moment of inertia are?

RankGuru · Accepted Answer

1. **Base Formula**: Moment of inertia is defined for a point mass as $I = m r^2$.
2. **Dimensional Terms**:
   - Mass ($m$) = $[M]$
   - Radius squared ($r^2$) = $[L^2]$
3. **Result**: The dimensional formula for moment of inertia is **$[ML^2]$**.
4. **Extension**: This holds for any rigid body since the integral $\int r^2 \, dm$ sums $[L^2][M]$ terms.

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dimensional analysis (moment of inertia)

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