Equilibrium: no resultant force AND no resultant torque

5 minAS Level4.2.2

AI-drafted, independently checked · not yet teacher-reviewed

By the end of this lesson

By the end you can state the two conditions for equilibrium, explain why both are needed, and use them together to find unknown forces.

Balanced forces, still spinning

Two kids push a playground roundabout with equal forces in opposite directions, on opposite sides. The forces cancel, yet the roundabout spins faster and faster.

Zero resultant force is not enough for equilibrium.

Definition

Equilibrium

An object is in equilibrium when:

the resultant force on it is zero, and
the resultant torque (resultant moment) on it is zero.

Then its velocity doesn't change and it doesn't start, or stop, turning. Most AS problems are about objects at rest.

What each condition rules out

Condition	Without it, the object…
no resultant force	accelerates: its centre of gravity speeds up, slows down or changes direction
no resultant torque	starts to rotate, or changes how fast it rotates

For forces in one plane, "no resultant force" is two checks: total force left = total force right, and total force up = total force down.

Two ways to fail

A couple: resultant force zero, resultant torque not zero. It spins.
A single push through the centre of gravity: no torque about G, but a resultant force. It accelerates without turning.

Equilibrium needs both boxes ticked.

Quick check

Fill in the blanksQuestion 1 · Recall

Multiple choiceQuestion 2 · Recall

Answer the 2 questions above to continue.