Is moment of inertia a scalar quantity ?

Answer

**Step-by-Step Solution:**

1. **Definition of Moment of Inertia**:
The moment of inertia (I) of a body is defined as 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. Mathematically, for a point mass \( m \) at a distance \( r \) from the axis, it is given by:
\[ I = m \cdot r^2 \]

2. **Nature of Moment of Inertia**:
The moment of inertia is a measure of an object's resistance to changes in its rotational motion. It is analogous to mass in linear motion, which measures resistance to changes in linear motion.

3. **Scalar Quantity**:
A scalar quantity is defined as a quantity that has only magnitude and no direction. In the case of moment of inertia:
- The mass \( m \) is a scalar quantity (it has only magnitude).
- The distance \( r \) is also a scalar quantity (it has only magnitude).
- The square of the distance \( r^2 \) remains a scalar.

4. **Product of Scalars**:
Since the moment of inertia is the product of mass and the square of the distance from the axis of rotation, and both components are scalar quantities, the result is also a scalar quantity:
\[ I = m \cdot r^2 \quad \text{(scalar)} \]

5. **Conclusion**:
Therefore, we conclude that the moment of inertia is indeed a scalar quantity because it has only magnitude and no direction.

**Final Answer**: Yes, the moment of inertia is a scalar quantity.

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