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

Compare mass and moment of inertia to build intuition. Mass is a pure scalar. It never changes no matter which direction you push the object.

1. Moment of inertia, on the other hand, can change value if you rotate the body about a different axis through the same point, even though the mass distribution has not changed.
2. Because its value depends on axis direction, one single number is not always enough to describe it in three dimensions.
3. Physicists use a 3 by 3 matrix, called the inertia tensor, which connects angular velocity to angular momentum for any axis you choose.
4. A quantity that needs this kind of matrix representation, linking one vector to another vector through directional coefficients, is classified as a tensor.

This general behavior is why moment of inertia is formally called a tensor quantity, matching option D.

A phasor represents time varying sinusoidal signals and has no link to rotational mass distribution, ruling out option A. Calling it a pure scalar ignores how its value shifts with axis direction, ruling out option B. Calling it a plain vector ignores that it needs a full matrix, not just one magnitude and one direction, ruling out option C.