2021 A/L Physics Past Paper · Question 15 (English Medium)

Answer: (3) Only (A) and (B) are true.

What the question asks

Find which of the statements (A), (B) and (C) are true.

All three are about what the moment of inertia of a body depends on.

Relevant theory

The mass of a body is a measure of its reluctance to any change of linear motion. The corresponding property for rotational motion is called moment of inertia.

The quantity I is called the "moment of inertia" of the object about the axis of rotation. "I" depends on the position of the axis of rotation and how the mass of the body is distributed about it.

Reading the options

The options are combinations of (A), (B) and (C).

We test each statement on its own.

The moment of inertia of a body is:

$$I = \sum m_i r_i^2$$

Reasoning and calculation

It depends on mass of the body.

Every particle adds $m_i r_i^2$ to the sum. More mass at the same distances gives a larger $I$.

A

It depends on mass distribution of the body.

The same mass has a larger $I$ when it is farther from the axis, because $r_i$ is squared. So the way the mass is spread matters.

B

It depends on angular velocity of the body.

The angular velocity $\omega$ does not appear in $I = \sum m_i r_i^2$. The body has the same $I$ at rest or spinning.

C

The moment of inertia depends on the mass and on how it is spread about the axis.

It does not depend on how fast the body spins.

So (A) and (B) are true, and (C) is false.

Why the other options fail

(B) is also true, so (A) alone is not enough.

(A) is also true, because more mass means a larger moment of inertia.

(C) is false and (A) is left out.

(C) is false, so not all three are true.

Conclusion

(A) and (B) are true. (C) is false.

The answer is (3).

The moment of inertia is for the body and the axis. It is the rotational counterpart of mass.

It does not change with the angular velocity.

Exam tip