Mistake Master

Torque and Work

▶︎  Watch it animatedinteractive step-through · ~3 min · optional

A 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.

TORQUE AND WORK W = ∫ τ dθ Work is the area under the torque, not τ times the angle. θ F τ = F R, turning through θ θ τ τ Δθ W = area work : area under τ-vs-θ power : P = τ ω
A torque turning a wheel through an angle does work. When τ varies with θ, that work is the area under the τ-vs-θ curve, W = ∫ τ dθ, not the constant-torque rectangle τ Δθ. Below the axis the area is negative: a braking torque does negative work.
The work under the torque · Open the sandbox →

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

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.

Skill check · 10 scenarios
Diagnostic
10-item topic check

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.

Not started · 10 items · ~15 min
Targeted Practice
Drill a single misconception

Pick one mistake you keep making and drill it on its own. Two correct in a row clears it and you move on.

Take the diagnostic to identify your misconceptions