A.4.1 (HL)—Torque

Torque is a turning effect

The torque of a force about an axis is

$\tau=Fr\sin\theta$

where $r$ is the distance from the axis to the point of application and $\theta$ is the angle between $\vec r$ and $\vec F$ .

Use the perpendicular lever arm

Equivalently, torque equals force multiplied by the perpendicular distance from the axis to the force’s line of action.

Choose a rotation sign

Clockwise and anticlockwise torques have opposite signs. Add torques about the specified axis rather than adding their magnitudes blindly.

Worked example from local Question Bank row 37867

Two forces produce the same rotational sense: $50\,\mathrm{N}$ at a perpendicular distance $0.50\,\mathrm{m}$ and $40\,\mathrm{N}$ at $0.20\,\mathrm{m}$ .

$\tau_{net}=(50)(0.50)+(40)(0.20)=25+8=33\,\mathrm{N\,m}\approx30\,\mathrm{N\,m}$

If one force acted in the opposite sense, its torque would enter with the opposite sign.

Common trap

A force through the axis has zero torque, even if its magnitude is large.

How it is assessed

The evidence asks for torque on an accelerating disk, rewarding the moment-of-inertia calculation followed by rotational Newton’s second law.

Command terms

Calculate

What earns marks

Use the perpendicular lever arm or τ=Fr sinθ. If angular acceleration is involved, find moment of inertia and then use τ=Iα. State the axis and sign convention.

Watch for

Using the full radius when the force’s line of action has a smaller perpendicular distance.

Representative question

[Maximum number: 2]

Calculate the torque that acts on the disk while it accelerates.

ALTERNATIVE 1
$\begin{aligned} & I=\frac{1}{2} \times 0.2 \times 0.4^{2}=<0.016 \gg & \text { Torque }=<I x \alpha=>0.1<\mathrm{Nm} \gg \end{aligned}$

ALTERNATIVE 2
$\begin{aligned} & \Delta L=\frac{1}{2} \times 0.20 \times 0.40^{2} \times 12.5=0.20 \text { «Js» } & \Gamma=\frac{\Delta L}{\Delta t}=\frac{\frac{1}{2} \times 0.20 \times 0.40^{2} \times 12.5}{2.0}=0.10 \text { «Nm» } \end{aligned}$

Use of 6 gives an answer of 0.096 Nm .

Allow ECF from MP1

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.4.1 (HL)—Torque

Calculate Torque About an Axis

A.4.1 Exam Analysis

Assessment in practice

Retrieve the A.4 Rigid Body Mechanics Model

Question 1