5.1 Torque

What is torque?

Torque (τ) measures the ability of a force to rotate an object about an axis. It depends on the force's magnitude, where it's applied, and its direction: τ = rFsinθ, where r is the distance from the axis to the point of application and θ is the angle between r and F. Units: N·m.

Lever arm and maximizing torque

The lever arm (moment arm) is the perpendicular distance from the axis of rotation to the line of action of the force. Torque is maximized when force is applied perpendicular to the lever arm (θ = 90°) and at the greatest possible distance from the axis — this is why longer wrenches make it easier to loosen bolts.

Direction and sign of torque

Torque is a vector (using the right-hand rule) but in 1D rotational problems we assign signs: counterclockwise torques are positive, clockwise are negative. Multiple torques acting on a rigid body add algebraically; net torque determines whether and how the object's rotation changes, per Newton's second law for rotation.

Key terms

Torque (τ)

A measure of a force's ability to rotate an object about an axis; τ = rFsinθ, measured in N·m.

Lever arm

The perpendicular distance from the axis of rotation to the line of action of the applied force.

Maximum torque condition

Occurs when force is applied perpendicular (θ = 90°) to the lever arm, since sinθ = 1.

Sign convention for torque

Counterclockwise torques are positive; clockwise torques are negative.

Zero torque condition

Occurs when the force is applied parallel to the lever arm (θ = 0° or 180°), or if r = 0.

Try an AP-style question

A 20 N force acts perpendicular to a 0.5 m wrench. What is the torque?

1. 10 N·m
2. 20.5 N·m
3. 40 N·m
4. 0.025 N·m