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A.4.8 (HL)—Rotational Newton’s second law

Syllabus
First assessment 2025
Objective
—
Level
HL

Apply Rotational Newton’s Second Law

HL only

Torque–inertia relation

For rotation about a fixed axis,

τnet=Iα\tau_{net}=I\alpha

Connect translation and rotation

When a force drives a rotating body or pulley, write both the translational force balance and the rotational torque balance if the system has translating and rotating parts.

Worked example from local Question Bank row 31942

A 50 N50\,\mathrm{N} tangential force acts 2.0 m2.0\,\mathrm{m} from the axis of a system with I=450 kg m2I=450\,\mathrm{kg\,m^2}.

τ=Fr=(50)(2.0)=100 N m\tau=Fr=(50)(2.0)=100\,\mathrm{N\,m}
α=τI=100450=0.22 rad s−2\alpha=\frac{\tau}{I}=\frac{100}{450}=0.22\,\mathrm{rad\,s^{-2}}

The acceleration direction follows the signed resultant torque.

Common trap

Do not treat torque as force or use a moment of inertia that does not match the rotation axis.

A.4.8 Exam Analysis

HL only

Assessment in practice

2–4 marks
How it is assessed

The evidence includes a coupled blocks-and-pulley system and an angular-acceleration versus torque graph used to find moment of inertia.

Command terms

Show / Identify

What earns marks

Use τ=Iα for the rotating component and combine it with translational equations when masses accelerate linearly. From an α–τ graph, the gradient is 1/I.

Watch for

Reading the graph gradient as I instead of 1/I or omitting the torque contribution from the pulley.

Representative question

Question 1

[Maximum number: 1]

The graph shows how the angular acceleration α\alpha of a flywheel varies with torque τ\tau applied to the flywheel.

What is the moment of inertia of the flywheel?

A

0.20 kg m20.20 \mathrm{~kg} \mathrm{~m}^{2}

B

5.0 kg m25.0 \mathrm{~kg} \mathrm{~m}^{2}

C

40 kg m240 \mathrm{~kg} \mathrm{~m}^{2}

D

80 kg m280 \mathrm{~kg} \mathrm{~m}^{2}