A.4.3 (HL)—Unbalanced torque

Rotational second law

A non-zero resultant torque causes angular acceleration:

$\sum\tau=I\alpha$

Use the chosen axis

Calculate signed torques about the specified axis and use the moment of inertia about that same axis. The direction of $\alpha$ follows the resultant torque.

Common trap

Do not use translational $F=ma$ for a purely rotational equation or mix an inertia about one axis with torque about another.

How it is assessed

The evidence asks for angular acceleration of a disk from angular displacement and time, and includes an unrelated fibre calculation as a distractor context; focus on the rotational objective evidence.

Command terms

Calculate / Determine

What earns marks

Find the angular displacement or torque relation from the diagram, then use the relevant rotational equation. Keep radians, seconds and the moment of inertia about the stated axis consistent.

Watch for

Using linear displacement or speed in a rotational equation, or failing to convert degrees/revolutions into radians.

Representative question

[Maximum number: 3]

Calculate the angular acceleration of the disk.

ALTERNATIVE 1
use of rotational kinematics equation to get $\alpha=\frac{2 \theta}{t^{2}}$ $\theta=<\frac{1.5}{0.555}=>27.3<\mathrm{rad} \gg$ $\alpha=\frac{2 \times 27.3}{0.96^{2}}=>59$ «rad $s^{-2}$ »
ALTERNATIVE 2
final speed $\mathrm{v}=2 \times 1.5 / 0.96=3.12 \mathrm{~ms}^{-1}$
final angular speed $\omega=\mathrm{v} / \mathrm{R}$ $\alpha=\omega / 0.96=59$ «rad s ${ }^{-2}$ »
ALTERNATIVE 3
acceleration $=2 \mathrm{~L} / \mathrm{t}^{2}$
acceleration $=3.26 \mathrm{~m} \mathrm{~s}^{-2}$
angular acceleration = acceleration/R =59 <rad s- $\mathrm{s}^{-2}$ »

Marking guidance:

Award [3] for bald correct answer from
interval 58.0 to 59.3.

Torque and rotation

Use $au=Fr\sin heta$ , $\sum au=0$ for rotational equilibrium and $\sum au=Ilpha$ for angular acceleration. Always state the axis and use the matching moment of inertia.

Describe angular motion

Use angular displacement, angular velocity and angular acceleration; rotational SUVAT applies only for uniform $lpha$ . Point-mass inertia is $I=\sum mr^2$ .

Track angular momentum

$L=I\omega,\quad \Delta L= au\Delta t$

Conserve angular momentum only when external resultant torque is negligible.

Track rotational energy

$E_{rot}= rac12I\omega^2$

For rolling or coupled systems, include translational and rotational energy separately.

A.4.3 (HL)—Unbalanced torque

Turn Unbalanced Torque into Angular Acceleration

A.4.3 Exam Analysis

Assessment in practice

Retrieve the A.4 Rigid Body Mechanics Model

Question 1