Mistake Master
Mistake Master · AP Physics C · Unit 6 · Topic 6.2 · Step-Through Animation
Torque and Work: The Area, Not the Product
You'll learnthat a changing torque's work is the area under τ-vs-θ, not torque times angle.
A torque turning a wheel through an angle does work. When the torque changes as it turns, the work is not τ times the angle — it is the AREA under the τ-vs-θ curve, W = ∫τ dθ. The constant-torque rectangle is only the special case; the rate of that work is the power, P = τω.
WORK LEDGER
Before you start
What you're looking at
A wheel driven through 3 radians by a torque that grows as it turns, beside a τ-vs-θ graph.
The question
How much work does a torque do when it changes as the wheel turns?
Watch for
The area filling under the τ-vs-θ curve — not the ghost rectangle of the tempting 18 J.
What the symbols mean
Horizontal axis is angular displacement θ (rad); vertical is torque τ (N·m); shaded area is work (joules).
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