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 4.2\" 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 35 mi/hr? Report answer accurate to 3 decimal places. (b) You buy new 5.25\" tires and drive at a constant speed of 50 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? Report answer accurate to the nearest whole number.

*Please show all work

Solution

Dia of Wheel = 14 + 4.2 +4.2 (rubber from both sides)

= 22.8 \"

Circumefernce of wheel = 2pi*r = 2pi*(22.8/2)

= 71.63 inches

a) Speed = 35 mi/hr

= 616 inch/sec

In 1 sec wheel travels 616 inches

So, no. of turns of wheel in 1 sec = distance traveled by wheel/circuference of wheel

= 616/71.63 = 8.599 rotations by wheel

b) Dia of wheel = 5.25 inches

Cicumference = 2pi*(5.25/2) = 16.49 inches

linear speed = 50 mph = 880 inch/sec (covert into inch/sec)

Rotations per sec of wheel = 880/16.49 = 53.36 rotations

So, wheel was moving at 53 rotations/sec