Angular Impulse Is the Area Under Torque-vs-Time

You'll learnthat angular impulse — the area under torque-vs-time — is what changes angular momentum.

A torque leans on a wheel for a few seconds. What it changes isn’t energy — it’s angular momentum, ΔL = ∫τ dt, the signed area under the torque-vs-time curve. The rectangle τΔt is only the constant-torque shortcut; watch what happens when the torque ramps — and why integrating over angle instead would have paid a different ledger.

8 STEPS · 6 QUICK CHECKS · v2

SPIN LAB

Before you start

What you're looking at

A wheel at rest pulled by a tangential string, a torque-vs-time graph, and a pink angular-momentum bar.

The question

How much does the torque change the wheel's angular momentum?

Watch for

The area under the torque-vs-time curve growing — that area is the change in L, not τΔt.

What the symbols mean

Pink marks angular momentum L (kg·m²/s); graph axes are torque τ versus time t; the area equals ΔL.

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