AP® Physics C: Mechanics · Unit 5 · Topic 5.5
Rotational Equilibrium
Rotational equilibrium means a rigid body has zero net force and zero net torque, so it neither accelerates nor spins up. Setting net torque about any pivot to zero lets you solve for unknown forces, like support forces or balance positions.
A seesaw balances when the torques trying to rotate it one way exactly cancel the torques trying to rotate it the other way. A heavy kid close to the pivot can balance a light kid far from the pivot because torque depends on both the force and the distance from the pivot: torque equals force times lever arm. Weight alone does not decide the outcome, weight times distance does.
This is useful because torque equations contain forces you cannot always get from Newton's second law alone. A beam resting on two supports has two unknown support forces, but force balance in the vertical direction only gives you one equation. Setting net torque about one of the supports to zero gives a second equation, and it conveniently removes that support's own force from the equation entirely, since its lever arm about itself is zero. Pick the pivot that eliminates the unknown you do not want, and the remaining force drops out algebraically.
Rotational equilibrium sits right after rotational dynamics because it is the special case where net torque is zero instead of equal to I times angular acceleration. It connects forward to statics problems with ladders, cranes, and hinges, where you combine force balance and torque balance together. The key habit carried forward is choosing a smart pivot: torque balance alone pins down forces, but true equilibrium always needs both zero net force and zero net torque checked together.
Key terms
- Torque
- The rotational effect of a force, equal to force times the lever arm distance from the pivot.
- Lever arm
- The perpendicular distance from the pivot to the line along which a force acts.
- Static equilibrium
- A state where a rigid body has both zero net force and zero net torque, so it stays at rest.
- Pivot point
- The reference point chosen for computing torques, often placed at an unknown force to eliminate it from the equation.
Watch it explained
- How it worksHow does setting the net torque to zero pin down a force you could not otherwise find?
- Worked exampleFind where a 60 kg person must sit to balance a 40 kg person sitting 2 m from the pivot.
- Worked exampleFind both end-support forces under a uniform 30 kg beam 4 m long carrying a 100 kg load 1 m from its left end.
- Common mistakeWhy isn't zero net force enough on its own to keep a rigid body from spinning up?
Check yourself
End of topic.