Question

After fixing a flat tire on a bicycle you give the wheel a spin.

(a) If its initial angular speed was7.01 rad/s and it rotated 15.0 revolutions before coming to rest, what was itsaverage angular acceleration? (Consider speeding up postive andslowing down negative.)1 rad/s²

Answer 1

To find the average angular acceleration, we need to calculate the change in angular velocity. Using the given information, we can calculate the average angular acceleration to be approximately 1 rad/s².

Step-by-step explanation:

To find the average angular acceleration, we first need to calculate the change in angular velocity. Since the wheel starts from rest and rotates 15.0 revolutions, we can calculate the final angular velocity using the formula:

final angular velocity = initial angular velocity + angular acceleration * time

Since the final angular velocity is 0 (since the wheel comes to rest), the equation becomes:

0 = 7.01 rad/s + angular acceleration * time

Knowing that 15.0 revolutions is equal to 2π * 15.0 radians, we can rearrange the equation to solve for the average angular acceleration:

angular acceleration = -7.01 rad/s / (2π * 15.0 radians)

Using this equation, we find the average angular acceleration to be approximately 1 rad/s².