A bicycle wheel of radius 0.35 m is spinning freely while the bike is supported off the ground. At one instant the wheel is observed to be rotating at 210 rev/min.
a. Part 1: Convert the rotation rate of 210 rev/min to angular speed in rad/s, showing your work.
b. Part 2: Determine the linear speed of a point on the outer surface of the tire at this instant, assuming the tire does not slip with respect to the road.
c. Part 3: A different racing wheel of radius 0.30 m is later installed. Calculate the angular speed, in rev/min, that this smaller wheel must have so that the bicycle moves forward at the same linear speed found in part (b).