Unit 06 — Rotation & Oscillation

Torque & Rotation

This page covers the core ideas now; worked examples and practice problems will keep expanding.

1. Torque

Torque is the rotational equivalent of force — it's what causes angular acceleration, the same way force causes linear acceleration. Force alone isn't enough to predict rotation; where the force is applied matters just as much as how big it is.

r distance from the pivot/axis to where the force is applied (m).
F applied force (N).
θ angle between the force vector and the lever arm.

τ = rF sin θ

Misconception

"A bigger force always produces more torque." False if it's applied closer to the axis, or at a shallow angle — a small force applied far from the pivot, perpendicular to the lever arm, can produce more torque than a large force applied right next to the axis.

2. Moment of Inertia

Moment of inertia, I, is rotational mass — an object's resistance to angular acceleration. Unlike ordinary mass, it depends not just on how much mass an object has but on how that mass is distributed relative to the axis of rotation. The same mass spread farther from the axis means a larger I.

τ = Iα

This is the rotational version of F = ma.

3. Angular Momentum

L = Iω

Angular momentum is conserved in a system with no external torque — this is why a spinning skater speeds up when pulling their arms in: I decreases, so ω must increase to keep L constant.

4. Practice Problems

1. A 10 N force is applied perpendicular to a wrench, 0.25 m from a bolt. Find the torque.

τ = rF sin90° = 0.25 × 10 × 1 = 2.5 N·m.