5.5 Rotational Equilibrium

What Rotational Equilibrium Means

An object is in rotational equilibrium when the net torque acting on it equals zero (Στ = 0). This means the object's angular acceleration is zero, so it is either not rotating or rotating at a constant angular velocity. Rotational equilibrium can occur alongside translational equilibrium (ΣF = 0), giving full static equilibrium.

Setting Up Torque Balance Problems

To solve equilibrium problems, choose a pivot point (often where an unknown force acts, to eliminate it from the equation), identify all forces and their lever arms, and set clockwise torques equal to counterclockwise torques. Remember τ = rFsinθ, where θ is the angle between the force and the position vector from the pivot.

Choosing the Pivot Wisely

The choice of pivot point is arbitrary—equilibrium equations hold true no matter where you place it—but a smart choice simplifies math. Placing the pivot at the location of an unknown force makes its torque zero (since r = 0), letting you solve directly for other unknowns without extra algebra.

Key terms

Rotational equilibrium

A state where the net torque on an object is zero (Στ = 0), resulting in zero angular acceleration.

Static equilibrium

A condition where both net force (ΣF = 0) and net torque (Στ = 0) are zero; the object is not accelerating linearly or angularly.

Pivot point choice

Any point can be chosen as the pivot for torque analysis; choosing it at an unknown force's location eliminates that force from the equation.

Torque formula

τ = rFsinθ, where r is the distance from pivot to force application point, F is force magnitude, and θ is the angle between them.

Balancing torques strategy

Set the sum of clockwise torques equal to the sum of counterclockwise torques about a chosen pivot to solve for unknowns.

Try an AP-style question

A 30 kg child sits 2 m from a seesaw's pivot. Where should a 20 kg child sit on the other side to balance?

1. 2 m from the pivot
2. 4 m from the pivot
3. 3 m from the pivot
4. 1.3 m from the pivot