Question

A bicycle tire is spinning clockwise at 2.10 rad/s. During a time period Δt = 1.65 s, the tire is stopped and spun in the opposite (counterclockwise) direction, also at 2.10 rad/s. Calculate the change in the tire's angular velocity Δω and the tire's average angular acceleration αav. (Indicate the direction with the signs of your answers.)

Answer 1

The change in the tire's angular velocity is -4.20 rad/s and the tire's average angular acceleration is -2.55 rad/s².

Step-by-step explanation:

To calculate the change in the tire's angular velocity Δω, we can subtract the initial angular velocity from the final angular velocity. In this case, the initial angular velocity is 2.10 rad/s and the final angular velocity is -2.10 rad/s. So, the change in angular velocity is -2.10 - 2.10 = -4.20 rad/s.

To calculate the tire's average angular acceleration αav, we can use the formula αav = Δω / Δt, where Δt is the time period. In this case, Δω is -4.20 rad/s and Δt is 1.65 s. So, the average angular acceleration is -4.20 / 1.65 = -2.55 rad/s².