CLASSICAL MECHANICS & THERMODYNAMICS - Chapter 5, Exercise 2 Solution
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Torque on a Bicycle Pedal

PROBLEM
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A cyclist applies a force of 250 N to a bicycle pedal, perpendicular
to the 0.17 m pedal crank arm. Calculate the torque produced.

SOLUTION
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Using the torque formula:

    tau = r F sin(theta)

Substitute the given values:

    r = 0.17 m
    F = 250 N
    theta = 90 degrees (force is perpendicular to the crank arm)

    tau = 0.17 x 250 x sin(90 degrees)
    tau = 0.17 x 250 x 1
    tau = 42.5 N.m

ANSWER: The torque produced is 42.5 N.m.

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WHY THIS WORKS AS AN ANSWER

Because the force is applied perpendicular to the crank arm (theta =
90 degrees), sin(90 degrees) = 1, so the full force contributes
entirely to rotation with none of it "wasted" - the same reasoning
used for the chapter's own wrench example. This is also exactly why
cyclists are taught to push perpendicular to the pedal crank through
the power stroke of a pedal rotation: any component of force that
isn't perpendicular to the crank arm (for example, pushing straight
down when the pedal is at the very top or bottom of its circle)
produces less torque, or even none at all, for the same physical
effort.