Your cars speedometer is geared to accurately give your spee

Your car\'s speedometer is geared to accurately give your speed using a certain tire size: 14\" diameter wheels (the metal part) and 4.65\" tires (the rubber part).

(a)   If your car\'s instruments are properly calibrated, how many times should your tire rotate per second if you are travelling at 65 mi/hr?
rotations = __________
Report answer accurate to 3 decimal places.

(b)   You buy new 5.4\" tires and drive at a constant speed of 70 mph (according to your car\'s instrument). However, a cop stops you and claims that you were speeding. How fast did the radar gun clock you moving?
actual speed = ____________

Solution

a)

Assuming the total tire diameter is 14 in + 2*4.65 in = 23.3 in, its circumference will be approximately 146.40 in. At 65 mph, the circumferential speed of the tire is 1056 in/s, so the rotation rate is
.. (1056 in/s)/(146.4 in/rev) = 7.2 rev/s.

b)

We know C = 2r.

Your speedo works correctly when 1 revolution = 2(14 + 2*4.65) = 46.6

With your new wheels, 1 revolution is 2(14 + 2*5.4) = 49.6 inches.

SO, when the speedo said you had travelled at the rate of 65 miles in 1 hour, you were actually travellling at 49.6/46.6 * 70 74.5 mph.