Hi! could you help this problem please try so many time but, the answer is not correct.
Question:The tires on a new compact car have a diameter of 2.0 ft and are warranted for 62,000 miles.
(a) Determine the angle (in radians) through which one of these tires will rotate during the warranty period.
physic - drwls, Sunday, November 15, 2009 at 1:46am
Each revolution moves the car pi*D = 6.283 feet
62000 miles is 327,360,000 feet
The number of revolutions is 5.210*10^7.
The number of radians is 2 pi times that... over 300 million
Hi! so you mean I have take 5.210*10^7 mutilply by 2 pi and than divide by 300 million. Just want to clarify thank you.
When I wrote "over 300 million", I was giving you an estimate of the number of radians. You do NOT divide by 300 million.
Answer
Yes, that's correct! To determine the angle through which one of the tires will rotate during the warranty period, you need to calculate the number of revolutions the tire will make and then convert that to radians.
1. Start by finding the distance covered by each revolution. The formula to find the circumference of a circle is C = πd, where C is the circumference and d is the diameter. In this case, the diameter is given as 2.0 ft, so the circumference is π * 2.0 ft = 6.283 ft.
2. Next, convert the 62,000 miles into feet. Since 1 mile equals 5,280 feet, the total distance covered by the warranty period is 62,000 miles * 5,280 ft/mile = 327,360,000 ft.
3. Divide the total distance by the circumference of each revolution to find the number of revolutions the tire will make: 327,360,000 ft / 6.283 ft/rev = 52,100,000 rev.
4. Finally, convert the number of revolutions to radians. Since one revolution is equal to 2π radians, multiply the number of revolutions by 2π: 52,100,000 rev * 2π rad/rev ≈ 327,361,083 rad.
So, during the warranty period, one of these tires will rotate approximately 327,361,083 radians.