Question 1126351: A vehicle has tires that are 75 cm in diameter. A point is marked on the edge of the tire.
A) determine the mesure of the angle through which the point turnes every second if the vehicle is travelling at 110 km/hr. Give your answer in degrees and in radians, to the nearest tenth.
B) what is the answer in radians If the diameter of the tire is 66 cm? Do you think that tire diameter affects tire life? Explain.
Found 2 solutions by josmiceli, Theo:
Answer by josmiceli(19441)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! the diameter of the tires is 75 cm.
the radius of the tires is half that which makes them equal to 75/2 cm.
the circumference of a circle is 2 * pi * r.
the circumference of the tires is therefore 2 * pi * 75/2 = 75 * pi.
the car travels 110 kilometers per hour.
multiply that by 1000 and the car travels 110,000 meters per hour.
multiply that by 100 and the car travels 11,000,000 centimeters per hour.
divide that by 3600 and the car travels 3055.5555555... centimeters per second.
the circumference of the tires is 75 * pi.
divide 3055.55555555... by 75 * pi and the tire makes 12.9681805482 complete revolutions every second.
multiply that by 360 and the angle which the point on the tire turns every second is 4668.544997 degrees.
multiply that by pi / 180 and the angle which the point on the tire turns every second is 81.48148148 radians.
if the diameter of the tire were 66 cm rather than 75 cm, then the radius would be 33 cm and the circumference would be 66 * pi.
the distance traveled by the car each second is the same at 3055.55555..... cm per second.
the number of revolutions of the tire each second is therefore 3055.55555..... / (66 * pi) = 14.7365688.
the number of degrees the mark on the tire goes through every second is therefore 14.7365688 * 360 = 5305.16477.
the number of radians is equal to that * pi / 180 = 92.59259259 radians.
the smaller diameter tire makes more revolutions for the same distance traveled which means the mark on the tire goes through more degrees / radians.
this should result in more wear on the tire, all other factors being equal, which should result in a shorter tire life.
note that you didn't really need the degrees that the mark on the tire went through.
just knowing that the smaller diameter tire makes more revolutions for the same distance should tell you that, all other things being equal, the smaller diameter tire will wear faster than the larger diameter tire.
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