Question

The tires on a new compact car have a diameter of 2.0 ft and are warranted for 62,000 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

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The tires on a new compact car have a diameter of 2.0 ft and are warranted for 64,000 miles.
(a) Determine the angle (in radians) through which one of these tires will rotate during the warranty period.
1 rad

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

Ans

The relation between distance traveled and the angle of rotation is

      ? = X /r

   Given

distance X = 64000mi

                  = 64000mi( 5280ft /mi)

Radius of the wheel r = D /2

                                    = 2f/2

                                    = 1f

Angle through which the typre rotates is

            ? = 64000(5280) /1ft

              = 3.3792x10^8 rad

   The number of revolutions made during 64000miles is

          ? = 3.3792x10^8 ( 1 rev / 2 ? rad)

            = 5.378x10^7 rev