Better not stop pedaling

Between doing physics problems on Brilliant, some people like to unicycle. A unicyclist is cycling up a hill angled \(15^\circ\) with respect to the horizontal. The center of mass of the cyclist is directly over the axle of the wheel and the cyclist/unicycle system have a combined mass of \(\SI{100}{\kilo\gram}.\) The radius of the wheel is \(\SI{0.5}{\meter}\) and the coefficient of static friction between the wheel and the asphalt is \(1.\)

What is the magnitude of the torque (in \(\si{\newton\meter}\)) that the cyclist needs to exert on the pedals in order to cycle up the hill at a constant speed?

Details and assumptions

• The unicycle does not slip against the hill.
• You may take the acceleration of gravity to be \(-\SI[per-mode=symbol]{9.8}{\meter\per\second\squared}.\)
• You may neglect air resistance.