Question

The tires on a new compact car have a diameter of 2.0 ft and are warranted for 57,000 miles.

(a) Determine the angle (in radians) through which one of these tires will rotate during the warranty period. rad

(b) How many revolutions of the tire are equivalent to your answer in (a)? rev

Answer 1

(a) Distance,

where L is the miles that is given under warranty period.

r is the radius of the car tire,

is the angle that is equivalent to cover the distance L.

Hence,

(b) The angle covered by the tire is going to get repeated once it completes the radians.

Hence, if we have to give this angle within this value, we can rewrite the total angle as the sum of the integral multiples of the and the residual angle, $Phi_0$ .

where n is the number of revolutions made by the car within the warranty period.

By substituting the total angle into the above formula, we can observe that,

Hence, the tire will have to finish 47.88 M (47.88 x 10⁶)revolutions in order to cover the warranted miles.