Diameter=2ft, The warranty of the tires is 60,000mi. How do you determine the angle in radians that will rotate during the warranty? How many revolutions are there of the tire?

Question

anonymous · Answer

Well we know that 1 revolution per minute = 360 degrees = 2*pi in radians right?

Now if you had to travel for 60,000 miles then you would divide that by the number by the circumference of the circle. imagine tearing a tire from one point and then laying it out flat. you will see that the circumference of the tire equals the distance travelled. Using this fact we get, 60000 miles / 2*pi * (2ft/2) = 4774.789. 

This means you will need to rotate your tire 4774.789 times to travel 60000 miles. In other words, you will your revolutions  = 4774.789.

Now to find the degrees that you will rotate your tire, simply multiply the revolutions * 2pi and that will be the total number of angle in radians that you will rotate your tire.