Calculating Tire Rotation in Radians and Revolutions - Homework Problem Solution

[sowmit]

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?)

 

[kuruman]

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?

 

[tomcue]

To calculate the angle in radians, you need to divide the distance traveled by the radius of the tire. In this case, the distance traveled is given as 3.2*10^9 feet and the radius is 1 foot. Plugging these values into the equation theta = s/r, we get theta = (3.2*10^9 feet / 1 foot) = 3.2*10^9 radians. This is equivalent to the answer given in the problem.

To find the number of revolutions, we need to divide the angle (in radians) by 2pi. So, the number of revolutions is (3.2*10^9 radians / 2pi) = 5.09*10^8 revolutions. This is equivalent to the answer given in the problem.

To find the angular velocity (omega), we can use the formula omega = v/r, where v is the linear velocity and r is the radius. In this case, the linear velocity is given as 3.2*10^9 feet per 60000 miles, which is equivalent to 3.2*10^9 feet per (60000 miles * 5280 feet) = 0.0108 feet per second. Plugging this value into the formula, we get omega = (0.0108 feet per second) / (1 foot) = 0.0108 radians per second.

I hope this helps with your problem. Let me know if you have any further questions.