KinexiaLEARN PHYSICS

Torque — Bicycle Pedal (Worked Example)

Medium
Problem

A cyclist pushes straight down on a pedal with 200 N. The crank arm is 0.17 m long and horizontal at that instant. What torque is applied to the chainring?

Given

  • r = 0.17 m

  • F = 200 N (perpendicular to crank)

Find

The torque τ.

Principle

With the crank horizontal and the push vertical, force and lever arm are perpendicular — maximum torque, τ = rF.

Formula

Solution

  1. Write the formula: τ=rF\tau = rF

  2. Substitute: τ=(0.17)(200)\tau = (0.17)(200)

  3. Multiply: τ=34 N⋅m\tau = 34\ \mathrm{N·m}

34 N·m

Unit check

m × N = N·m — correct.

What this means physically

34 N·m at the chainring — through the gears this becomes the driving force at the wheel. Standing on the pedals (full body weight) is how riders climb steep hills.

Common mistake

Using τ = rF when the crank is vertical. At top/bottom dead centre the force points along the crank (θ = 0), giving zero torque — the dead spot cyclists feel.