You are traveling forward in a car at 20 m/s. Your car tires have a radius of 33 cm. You slam on the brakes, which slows the tires at an angular acceleration of 40 rad/s^2. Through how many radians of rotation does each tire go from the time you slam on the brakes until the tires stop spinning?

Question

You are traveling forward in a car at 20 m/s. Your car tires have a radius of 33 cm. You slam on the brakes, which slows the tires at an angular acceleration of 40 rad/s^2. Through how many radians of rotation does each tire go from the time you slam on the brakes until the tires stop spinning?

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1 answer
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Answer 1

Bot GPT 3.5 answered

To find out how many radians of rotation each tire goes through, we first need to calculate the final angular velocity of the tires when they stop spinning.

The angular acceleration is given as 40 rad/s^2 and the initial angular velocity is 20 m/s / (0.33 m) = 60.606 rad/s (since angular velocity = linear velocity / radius).

Using the formula:

angular velocity^2 = initial angular velocity^2 + 2 * angular acceleration * angle

0 = 60.606^2 + 2 * 40 * angle

3600 = 80 * angle

angle = 45 radians

Therefore, each tire goes through 45 radians of rotation from the time you slam on the brakes until they stop spinning.