Question

Define moment of inertia of a rotating rigid body. State its SI unit and dimensions.

Hint:

Moment of inertia depends on mass distribution and axis; use standard formulas for common shapes (e.g., \( \frac{1}{2}MR^2 \) for a disc).

Answer 1

The moment of inertia (\( I \)) of a rotating rigid body is defined as the mass property that quantifies its resistance to angular acceleration about a given axis. It is the sum of the products of the mass of each particle in the body and the square of its distance from the axis of rotation: \( I = \sum m_i r_i^2 \), where \( m_i \) is the mass of the \( i \)-th particle and \( r_i \) is its perpendicular distance from the axis.
SI Unit: kilogram meter squared (\( \text{kg} \cdot \text{m}^2 \)).
Dimensions: Using \( [M] \) for mass, \( [L] \) for length: \[ [I] = [M][L]^2 = M L^2. \] Answer: Moment of inertia is the mass property resisting angular acceleration, \( I = \sum m_i r_i^2 \). SI unit: \( \text{kg} \cdot \text{m}^2 \), dimensions: \( M L^2 \).