Question

A car is traveling at 47 mph. If its tires have a diameter of 27 inches, how fast are the car's tires turning? Express the answer in revolutions per minute. Round to two decimal places

Answer 1

3676.44 rad/min

Explanation:

It is a problem about the angular speed of the car's wheel.

You can calculate the angular speed by using the following formula, which relates the tangential speed of the wheels (the same as the speed of the car) with the angular speed:

`\omega=(v)/(r)` ( 1 )

v: speed of the car = tangential speed of the wheels = 47mph

r: radius of the wheels = 27/2 in = 13.5 in

you change the units of the speed:

`47mph*(63360in)/(1mille)*(1h)/(60min)=49632(in)/(min)`

next, you replace the values of v and r in the equation (1):

`\omega=(v)/(r)=(49632in/min)/(13.5in)=3676.44(rad)/(min)`

Then, the car's tires are turning with an angular speed of 3676.44 rad/min