30-09-2017
Mathematics

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A train 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?

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barnuts barnuts

10-10-2017

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

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