Question

I need to find out how much power is generated by a stationary bike that has a pedal radius of 5 inches and is pedaled at a velocity of 75 revolutions per minute those are the only factors that need to be taken into account

Answer 1

This is not sufficient info to answer.
You need to know the 'force' exerted by the pedaller.

Power from a rotating system is given by[\[P=\tau \times \omega \]

Where tau = torque
and omega = angular velocity

Torque is calculated from \[\tau = F \times r\]
Where r is the radius and F is the tangential force acting at this radius.

You can see that you do not have enough information because it would be possible to pedal the same bike (were it not stationary) either along the flat or up a steep hill at the SAME rpm, but it is evident that more power is required to achieve the uphill climb.

Answer 2

If this is a real life question then it is more complicated, because you know that the force you exert when pedalling is greater when the pedal is horizontal, than when it is at the top or bottom of the crank. The equation for power is still true at any moment, but the average power over a run would depend on the way the cyclist pushes throughout the circular motion of the pedal.