Atrain wheel has a diameter of 30 inches to the rim, which rests on the track. the flange, which keeps the wheel from slipping off the track, projects 1 inch beyond the rim. when the train is traveling 60 mph, what is the linear velocity of a point on the outer edge of the flange?

The diameter of the wheel is 30 inches, therefore the radius is 15 inches.

We calculate the angular velocity (w) of this using the formula:

w = v / r
w = 60 mph / 15 inches = 4 mph / inches

Since the flange is 1 inch beyond the rim, hence the effective radius for this is 16 inches.So the velocity on the outer edge is:
v = w r 
v = (4 mph / inches) * 16 inchesv = 64 mph