Question 666771: Each tire of an automobile has a radius of 1.25 feet. How many revolutions per minute does a tire make when the automobile is traveling at a speed of 65 feet/sec?
Answer by DrBeeee(684)   (Show Source):
You can put this solution on YOUR website! This is too neat of a problem to pass up, so here goes! I hope I can explain the solution well enough for you.
First we want to calculate how far we travel with each revolution of the tire. It is the circumference of the tire. Agree?
Using
(1) Circumference = pi*d, where d is the diameter of the tire or 2.5 ft., we get
(2) Tire rotational distance per revolution = 2.5*pi ft/rev.
Now how fast is the car moving? It says 65 ft/sec which is
(3) Car Speed = 65 ft/sec or
(4) Car Speed = 60*65 ft/min or
(5) Car Speed = 3900 ft/min
Now we want the third/final calculation that gives us the tire rotational speed in revolutions per minute. This is given by
(6) Rotational Speed = (ft/min)/(ft/rev) or using (5) and (2) we get
(7) Rotational Speed = (3900 ft/min)/(2.5*pi ft/rev) or
(8) Rotational Speed = 1560/pi rev/min or
(9) Rotational Speed ~ 497 rev/min
Answer: The tire is rotating at the rate of approximately 497 revolutions per minute.
Note my use of what is called dimensional analysis to keep our calculations straight. For example, look at (6) where we have (ft/min)/(ft/rev) which, when evaluated is (ft/min)*(rev/ft) = rev/min, because ft cancels.
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