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 Question from Lindsay, a student: Determine the angular velocity, in radians per second, of a 14-inch car wheel, if the car is traveling at 60 miles per hour

Hi Lindsay,

The circumference of a 14 inch diameter circle is π times the diameter which is 16 π inches and 60 miles is

60 × 5280 × 12 inches.

Hence in 60 miles the tire will have rotated 60 × 5280 × 12/(16 × π) times. At 60 mph that's

60 × 5280 × 12/(16 × π) rotations/hour.

There are 60 minutes in an hour and 60 seconds in a minute so at 60 mph the tire makes

60 × 5280 × 12/(16 × π) rotations/hour × 1/60 hours/minute × 1/60 minutes/second

which is

60 × 5280 × 12/(16 × π × 60 × 60) rotations/second.

One rotation is 2 π radians so finally we have

60 × 5280 × 12/(16 × π × 60 × 60) rotations/second × 2 π/1 radians/rotation

or

60 × 5280 × 12× 2 π/(16 × π × 60 × 60) radians/second.

Harley

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.