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How many revolutions will a car wheel of diameter 28 in. make over a period of half an hour if the car is traveling at 60 mi/hr?
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
This is a good application of circular arc problems in getting the number of revolutions of a car wheel especially when you're driving a car. In this problem, the distance traveled is not given but the speed or velocity and time are given. If you know the speed and time,then you can calculate the distance traveled as follows
where S is the distance traveled, V is the speed or velocity, and t is the travel time. Substitute the values of V and t, we have
Since the radius of a car wheel is expressed in inches, then we have to convert the distance traveled by car in inches as follows
Finally, we can get the number of revolutions of a car wheel as follows
where S is the total distance traveled or total length of a circular arc, R is the radius of a circle, and θ is the total angle of a circular arc in radians. Radians is a unit less value of an angle.
Substitute the values of S and R in order to solve for the value of total angle, we have
Therefore, the number of revolutions of a car wheel is
