rotational equilibrium

Meaning: An object is in rotational equilibrium when the net torque on it is zero. Zero net torque means zero angular acceleration, so the object is either not rotating or rotating at constant angular velocity. A small force far from the pivot can balance a large force close to it. Static equilibrium requires rotational equilibrium plus zero net force.

Equation: Στ = Iα = 0, with τ = rF sinθ. Here τ is torque (N·m), I is moment of inertia (kg·m²), α is angular acceleration (rad/s²), r is the distance from the pivot to where the force acts (m), F is the force (N), and θ is the angle between r and F. Equivalently, clockwise torque = counterclockwise torque.

On the MCAT: Expect a seesaw, a beam on supports, a meter stick with hanging masses, or a forearm held level by the biceps. Pick the pivot at the point where an unknown force acts, so that force has no torque, then balance the remaining torques. A uniform beam's weight acts at its center.

Common confusion: Zero net force does not guarantee zero net torque. Two equal and opposite forces applied at different points form a couple that spins the object. Check force balance and torque balance separately.