About torque and moment of inertia

[russ_watters]

Historically, sprinters favor shorter crank arms while pursuit and time trial racers like longer crank arms. The physics apply but one variable I find missing or should I say underestimated, is how the longer crank arm affect human energy to move that longer arm through a single spindle rotation. Leaving acceleration aside, increased torque of a longer crank arm will require more energy per revolution than a smaller one. So, if cadence remains the same for longer and shorter arms, energy required to move the longer arm should be greater. If this is true, the commonly held notion that longer crank arms are better for time trial racers may not hold water.

No, the power required to move the bike is the same either way. A longer crank arm means a smaller force to achieve the same torque. A longer crank arm would allow you to provide more torque if needed for acceleration.