An automobile wheel has a diameter of 14 in. If the car travels at a speed of 55 mph, what is the angular velocity, in radians per hour, of a point on the edge of the wheel?

Expert Answers

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Use the formula

`omega=V/r`

where `w` is the angular velocity,  V is the linear speed and r is the radius of the wheel.

Convert r from inches to miles.

1 inch = 0.000016 miles

r= 14 in x 0.000016 miles/inch = 0.000224 miles

`omega=55 /0.000224=245,536` radians/hour

Thus the angular velocity is 245,535 radians/hour.

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