Torque and Work
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalA torque acting through an angle does work. When that torque changes as the wheel turns, the work is not τ times the angle. It is the area under the τ-vs-θ curve: W = ∫ τ dθ. The rate of doing that work is the power, P = τ ω.
This is the first Unit 6 topic that needs a real integral, so the slips are calculus slips. The common one: using τ Δθ when τ varies instead of integrating. Others mix up the work integral with the power τ ω, drop the sign when a torque brakes, or pair a force with an angular speed. Read the work off the curve as signed area, and match each part of the power formula to its own kind of motion.
The work
3 ways in · any order
Lesson
Torque and Work
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Rotational work as the area under the torque, W = integral of tau d theta, with rotational power P = tau omega. Covers when the constant-torque shortcut tau delta-theta fails, the sign of braking work, and how work differs from power. Closes with a ten-scenario skill check.
Diagnostic
10-item topic check
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Ten items across the four Topic 6.2 mistakes: using tau delta-theta for a torque that varies, confusing the work integral with power, dropping the sign or limits of the integral, and mismatching the partners in P = tau omega. Take it cold to see what still trips you up, or after the lesson to confirm it doesn't.
Targeted Practice
Drill a single misconception
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Pick one mistake you keep making and drill it on its own. Two correct in a row clears it and you move on.