Question

Moment of inertia is a

• A. Phasor
• B. Scalar
• C. Vector
• D. Tensor

Hint:

Think about whether one single number and direction can describe rotational inertia about every possible axis.

Answer 1

The Correct Option is D

Moment of inertia measures how the mass of a rigid body is distributed relative to a chosen axis of rotation, and it decides how much torque is needed to produce a given angular acceleration about that axis.

For rotation about a single fixed axis, moment of inertia behaves like a simple number, so at that basic level it can look scalar. But in general, a rigid body can rotate about any axis passing through a point, and the moment of inertia value changes depending on the direction of that axis. To fully describe rotational inertia for all possible axes through a point, we need a quantity that relates two vectors, angular velocity and angular momentum, and connects them in a way that also depends on direction. Such a quantity, represented by a matrix that transforms in a specific way with the choice of axes, is called a tensor. This is why moment of inertia is treated as a tensor quantity in a full mechanical description.

Option A is wrong because a phasor is used to represent quantities that vary sinusoidally with time, such as alternating current, and has nothing to do with mass distribution.

Option B is wrong because treating it as a plain scalar only works for rotation about one fixed axis, and fails to capture how the value changes with axis direction in general.

Option C is wrong because a vector is described by a single magnitude and one direction, but moment of inertia needs a full matrix of values to relate angular momentum and angular velocity in different directions, which a simple vector cannot do.

The correct answer is tensor.