Unit of moment of inertia in MKS system

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Accepted Answer

1. **Definition:** Moment of Inertia ($I$) is defined as the sum of the products of the masses of the particles ($m$) and the square of their perpendicular distances ($r$) from the axis of rotation, expressed as $I = \sum m_i r_i^2$ .
2. **Dimensional Formula:** The dimensions of mass are $[M]$ and length are $[L]$. Therefore, the dimensional formula for moment of inertia is $[ML^2]$ .
3. **MKS System:** In the MKS (Metre-Kilogram-Second) system, which corresponds to SI units for mechanical quantities, the unit of mass is the kilogram (kg) and the unit of length is the metre (m).
4. **Conclusion:** Substituting these units into the dimensional relationship yields the unit $	ext{kg m}^2$ .

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