A.4.2 (HL)—Rotational equilibrium

Equilibrium condition

A rigid body is in rotational equilibrium when the resultant torque about any chosen axis is zero:

$\sum\tau=0$

Balance clockwise and anticlockwise effects

Choose an axis, assign signs, and set the sum of clockwise torques equal to the sum of anticlockwise torques. A body can still have translational equilibrium as a separate condition.

Common trap

Zero resultant torque means no angular acceleration; it does not by itself prove that the net force is zero.

How it is assessed

The evidence asks directly for the condition for rotational equilibrium.

Command terms

State

What earns marks

State that rotational equilibrium requires zero resultant torque or zero net moment about the chosen axis. If the question also concerns rest, check translational equilibrium separately.

Watch for

Saying that every individual torque must be zero rather than that the signed resultant torque is zero.

Representative question

[Maximum number: 1]

State the condition for rotational equilibrium.

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.4.2 (HL)—Rotational equilibrium

Test Rotational Equilibrium

A.4.2 Exam Analysis

Assessment in practice

Retrieve the A.4 Rigid Body Mechanics Model

Question 1