Rotational Motion 3

Question

The tires on a new compact car have a diameter of 2.0 ft and are warranted for 60,000 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

Hi Dominic!

 

They key to this problem is that, if the rolling tires are not slipping, the car moves one tire circumference down the road for every tire rotation.  So, if you divide the number of miles of travel for the tire by the circumference of the tire, you will get the number of full revolutions the tire makes in its warranty lifetime.  Then, each revolution is 2π radians, so you can convert from number of revolutions to number of radians with that.

 

One thing to look out for in the first calculation is to make sure your length units are the same in each case.  So you should either convert 60,000 miles to feet, or 2 feet to miles (remember, when computing the circumference of the tire, that 2 feet is the diameter, not the radius).

 

See if that gets you started, and, if you have more questions, or would like to check an answer, just let me know!