Angular Impulse Is the Area Under Torque-vs-Time

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.

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