Calculating Tire Rotation in Radians and Revolutions - Homework Problem Solution

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To solve the homework problem, the angle in radians through which a tire rotates can be calculated using the formula theta = s/r, where s is the distance traveled and r is the radius of the tire. Given a tire diameter of 2.0 ft, the radius is 1.0 ft, and the total distance is 60,000 miles, which converts to 3.2*e^9 ft. The correct calculation for theta results in 3.2*e^8 radians, not 5.0*10^6 radians as initially stated. Additionally, to find the number of revolutions, one must determine how many circumferences fit into the total distance traveled, which relates to the concept of angular velocity (omega) in revolutions per second. Understanding these calculations is crucial for solving the problem accurately.
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Please help me with this problem??

Homework Statement



The question is:

the tires on a new car have a diameter of 2.0 ft and are warranted for 60000 miles (3.2*e^9 ft).

(a) Determine the angle (in radians) through which one of the tires will rotate?

(b) How many revolutions are equivalent to ur answer in part a?>

Homework Equations


theta = s/r


The Attempt at a Solution



theta = (3.2*e^9 ft / 1.0 ft) * (2pi radian/ 360 degree) = 5.0* 10^6 radian, but the answer says 3.2*e^8 radians. How's that possible.

How do I find omega (revolution per second?)
 
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When the wheel has moved forward by one circumference, it has rotated by 2π radians.
How many circumferences can fit in 60,000 miles?

Why do you want to find omega?
 

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