Rotation & Angular Dynamics · Physics

A force can twist: torque measures that turning effect.

Torque links forces to rotational change. Learn how lever arm geometry sets the size of torque, and how the right-hand rule sets its direction.

This topic

Torque

Understand torque as a vector, use the moment arm, then apply it to rotational equilibrium.

Definition

Torque as a vector

Torque measures the tendency of a force to rotate an object about an axis. It depends on both the force and where it is applied.

Core idea: τ depends on force and position
Vector form: τ = r × F (direction matters)
Magnitude: τ = rF sin(φ)
Units: N·m (not the same as energy)

Geometry

Lever arm and moment arm

The moment arm is the perpendicular distance from the axis to the line of action of the force. It is the simplest way to compute torque magnitude.

Line of action of a force
Perpendicular distance: r_⊥
Magnitude: τ = F r_⊥
Why pushing “more perpendicular” matters

Direction

Direction of torque (right-hand rule)

Torque has a direction along the rotation axis. Use the right-hand rule on r × F to determine the sign and axis direction.

Right-hand rule for cross products
Positive/negative torque in 2D problems
Choosing a consistent pivot sign convention
Common mistakes when forces are angled

Equilibrium

Net torque and rotational equilibrium

If net torque about an axis is zero, angular acceleration is zero about that axis. This is the core condition for static balance and many support-force problems.

Rotational equilibrium: Στ = 0
Why you can choose a convenient pivot
Balancing torques vs balancing forces
Solving typical beam and hinge problems

Practice

Practice & Exercises

Practice computing torque magnitudes and signs, then apply Στ = 0 in rotational equilibrium setups.

Compute τ from r × F and from moment arms
Right-hand rule sign checks in 2D
Static equilibrium: solve beam / lever problems
Combine ΣF = 0 and Στ = 0 correctly
Exam-style torque and balance sets