Better not stop pedaling

Between doing physics problems on Brilliant, some people like to unicycle. A unicyclist is cycling up a hill angled 15 degrees 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 100 kg. The radius of the wheel is 0.5 m and the coefficient of static friction between the wheel and the asphalt is 1. What is the magnitude of the torque 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 \(-9.8~m/s^2\).
• You may neglect air resistance.