In the past, bicycles used small bottle-shaped dc generators to power the headlight. A small wheel (the top of the “bottle”) in contact with a tire caused the shaft of the generator to rotate. Suppose the generator has 150 turns of wire in a circular coil of radius 1.8 cm. The magnetic field magnitude in the region of the coil is 0.20 T. When the generator supplies an emf of amplitude 4.2 V to the lightbulb, the lightbulb consumes an average power of 6.0 W and a maximum instantaneous power of 12.0 W. 

(a) What is the rotational speed in rev/min of the armature of the generator? 

(b) What is the average torque and maximum instantaneous torque that must be applied by the bicycle tire to the generator, assuming the generator to be ideal? 

(c) The radius of the tire is 32 cm, and the radius of the shaft of the generator where it contacts the tire is 1.0 cm. At what linear speed must the bicycle move to supply an emf of amplitude 4.2 V?