Final answer:
To find the number of revolutions the tire makes during the motion from rest to a speed of 22.0 m/s in 9.00 s, we need to calculate the distance traveled and the circumference of the tire. Assuming no slipping occurs, the tire does not make any revolutions. The final angular speed of the tire in revolutions per second is also 0 since the initial angular velocity is 0 and the time taken is 9 seconds.
Step-by-step explanation:
To find the number of revolutions the tire makes during this motion:
First, we need to find the distance traveled by the car. Using the formula: distance = initial velocity * time + 0.5 * acceleration * time^2, we can calculate the distance as follows:
distance = 0 * 9 + 0.5 * 0 * 9^2 = 0 m.
Next, we can find the circumference of the tire using the formula: circumference = 2 * pi * radius. Plugging in the values:
circumference = 2 * 3.14 * 0.58 m = 3.6476 m.
Finally, the number of revolutions can be found using the formula: number of revolutions = distance / circumference. Plugging in the values:
number of revolutions = 0 m / 3.6476 m = 0 revolutions.
To find the final angular speed of the tire in revolutions per second:
Since no slipping occurs, the final angular speed is equal to the initial angular speed, which is the angular displacement over the time taken.
Using the formula:
angular speed = angular displacement / time.
Given that the initial angular velocity is 0 revolutions per second and the time taken is 9 seconds, we can calculate the final angular speed as follows:
angular speed = 0 revolutions / 9 s = 0 revolutions per second.