State the formula for the moment of inertia of a point mass.

I = mr², where I is moment of inertia, m is mass, and r is the perpendicular distance from the axis of rotation.

Define the moment of inertia of a point mass in words.

The moment of inertia of a point mass is the product of its mass and the square of its perpendicular distance from the axis of rotation.

What does the symbol r represent in the equation I = mr² for a point mass?

The perpendicular distance from the mass to the axis of rotation.

Calculate the moment of inertia when mass = 3.6 kg, distance from axis = 0.4 m.

Moment of inertia = 3.6 × 0.4 × 0.4 = 0.576 kg m².

State the formula for the moment of inertia of an extended object.

I = Σmr², where the sum is taken over all constituent mass elements, each multiplied by the square of its perpendicular distance from the axis of rotation.

Explain why the moment of inertia of an extended object is calculated as a summation rather than a single product.

An extended object consists of many mass elements at different distances from the axis, so each element's contribution (mr²) must be summed to find the total moment of inertia.

AQA A-Level Physics 7408

Measurements and Their Errors

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Engineering Physics

Concept of moment of inertia

3 things to know
Paper 3, section B

Overview

Moment of inertia as resistance to angular acceleration, and why shape matters as much as mass.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Numbers

What does r stand for in I = mr², and how does total mass affect moment of inertia?

Key term

Why do a disc and a hoop of equal mass and radius differ in moment of inertia?

Key term

In rotational motion, what quantity plays the same role as mass does in linear motion?

Questions from this subtopic

Each one with the model answer underneath.

1
State the formula for the moment of inertia of a point mass.
Model answer
I = mr², where I is moment of inertia, m is mass, and r is the perpendicular distance from the axis of rotation.
2
Define the moment of inertia of a point mass in words.
Model answer
The moment of inertia of a point mass is the product of its mass and the square of its perpendicular distance from the axis of rotation.
3
What does the symbol r represent in the equation I = mr² for a point mass?
Model answer
The perpendicular distance from the mass to the axis of rotation.
4
Calculate the moment of inertia when mass = 3.6 kg, distance from axis = 0.4 m.
Model answer
Moment of inertia = 3.6 × 0.4 × 0.4 = 0.576 kg m².
5
State the formula for the moment of inertia of an extended object.
Model answer
I = Σmr², where the sum is taken over all constituent mass elements, each multiplied by the square of its perpendicular distance from the axis of rotation.
6
Explain why the moment of inertia of an extended object is calculated as a summation rather than a single product.
Model answer
An extended object consists of many mass elements at different distances from the axis, so each element's contribution (mr²) must be summed to find the total moment of inertia.

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