# Trigonometry

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A car with a wheel of radius 14 inches is moving with a speed of 55 mph. Find the angular speed of the automobile to the nearest mile per hour.

I got 55/14

• Trigonometry -

You've got to see that dividing 55mi/hr by 14in is a useless amount.

try to do a sanity check on your answer. Just because you have a number doesn't mean it's correct, or even reasonable.

55/14 is about 4. Surely you don't think a car going 55 mph has its wheels turning at 4 rev/hr!

Angular speed is measured in radians/sec. Since a full circle has 2pi radians, the angular speed is 2pi times the speed in rev/sec.

To get rev/sec, divide the distance traveled by the circumference of the wheel.

55 mi/hr * 5280ft/mi * 12in/ft * 1hr/3600sec = 968 in/sec

2pi*14 = 28pi in/rev

so, the angular speed is 968/28pi = 242/7pi rev/sec

Now multiply that by 2pi to get

• Trigonometry -

angular speed would have to be expressed as units of angle per unit of time, e.g. so many rotations per minute, or rpm.
It would not be measured in miles per hour

the circumference of the wheel is 2(14)π = 28π inches
55 mph = 55(5280)(12)
or 3484800 inches/hour
= 58080 inches/minute

so the angular speed = 58080/28π rotations per minute
= appr 660.27 rotations/min

what units would it be in ??

• Trigonometry -

Sorry the problem states find the angular speed of the wheel, not the car, in radians per second.

The way I derived my answer was through the linear speed formula (v = radius * angular speed) and so plugging in would yield (55 = 14x), but I do understand some conversions would be necessary.

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