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Question

A bike with 20 inch diameter wheels is traveling at 12mi/h.

Find the angular speed of the wheels in rad/min.

Enter exact answer.

How many revolutions per min do the wheels rotate?

Round your answer to three decimal places.

Answer 1

First find the circumference of the wheel:

c = πd = 20π in/revolution

Then convert the speed of the bike into inches per minute:

s = (12 mi/h) * (5,280 ft/mi) * (12 in/ft) * (1h/60 min) = 12,672 in/min

Then figure out how many rotations occur at this speed:

angular speed = (12,672 in/min) / (20π in/revolution) = 633.6/π revolutions/min = 201.681 revolutions/min

There are 2π radians in a rotation:

angular speed = (633.6/π rotations/min) * (2π rad/rotation) = 1,267.2 rad/min

Answer 2

1 mile = 5280 ft = 63360 inches

The wheel circumference = 2 πr = 20π inches

12 mi/h = 12 x 63360 / 60 inches per minute = 12672 inches per minute

Revolutions per minute = 12672 / 20π = 3168 / (5π). = 201.681

1 revolution = 2π radians

Radians per minute = (12672 / 20π) x 2π = 12672/ 10 = 6336/5 radians per minute