Tires on a car have a diameter of 2 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. b) How m,any revolutions of the tire are equivalent to your answer in, part a)? i have drawn a tire with the diameter and the Centripetal Acceleration.
in one revolution the tire goes 2 pi r = pi D feet = pi (2) feet
which is (2 pi/5280)miles
(2 pi/5280)n = 60,000 miles (part b)
2 pi n = number of radians (part a)
To determine the angle through which the tire rotates during the warranty period, we can use the formula for calculating the circumference of a circle, C = 2πr, where C is the circumference and r is the radius. Since the diameter of the tire is given as 2 ft, the radius would be half of that, which is 1 ft.
a) To find the angle in radians, we need to first find the total distance covered by the tire during the warranty period. We are given that the warranty is for 60,000 miles. Since we are dealing with feet (the units of the tire's diameter), we need to convert the distance from miles to feet.
There are 5280 feet in a mile, so 60,000 miles would be:
60,000 miles * 5280 feet/mile = 316,800,000 feet
Now we can calculate the angle in radians. The formula to find the angle is:
angle = distance / radius
angle = 316,800,000 feet / 1 foot = 316,800,000 radians
Therefore, one of these tires will rotate approximately 316,800,000 radians during the warranty period.
b) Next, we need to determine how many revolutions of the tire are equivalent to the angle calculated in part a). Since one revolution is equal to 2π radians, we can calculate the number of revolutions by dividing the angle in radians by 2π.
number of revolutions = angle / (2π)
number of revolutions = 316,800,000 radians / (2π) ≈ 50,484,817 revolutions
So, approximately 50,484,817 revolutions of the tire are equivalent to the angle calculated in part a).