Question

Is moment of inertia is a scalar quantity?

Answer 1

Hint: Inertia word means resistance or opposition. While means only magnitude not direction. In classical mechanics the moment of inertia is also known as angular mass. By this you can identify whether angular mass is scalar or vector and same goes for moment of inertia.

Complete step by step solution:
Answer is yes, the moment of inertia is a scalar quantity. If you will see the terms in formula, these are mass and square of distance i.e., r. Mass is a scalar quantity and distance is also scalar quantity and the square itself has no direction. So the product of scale and scale gives scalar quantity only. Therefore the moment of inertia is a scalar quantity.
Moment of inertia: if a rigid body about an axis of rotations given by sum of the product of masses of particle constituting body and squares of their perpendicular distances from axis of rotation.
$I=\sum _{i=1}^n{m}_i{r}_i^2$
From above equation it is obvious that I depends on following factor,
Position of particle from an axis of rotation
Shape and size of body
Orientation of the axis of rotation
Distribution of mass
Throughout the theory we didn’t mention direction for any term. Hence we can conclude the moment of inertia doesn't have direction. Therefore it is a scalar quantity.

Additional information:
Moment of inertia is an inherent property of anybody. It basically depends on the distribution of mass of the body that measures its resistance to rotational acceleration about a given axis. An object rotating at constant angular velocity will remain rotating unless acted upon by an external torque. In this way the moment of inertia plays the same role in rotational dynamics as mass does in linear dynamics.

Note: In classical mechanics moment of inertia is known as mass moment of inertia, rotational inertia, polar moment of inertia, or angular mass. All this quantity doesn't have direction; it only has magnitude.