An electric grinder is spinning counterclockwise (CCW) at 33 revolutions per second (rev/s) when the power is turned off. The grinder slows at a steady rate, taking 89 seconds to stop rotating. Taking CCW rotations as positive, what was the average angular acceleration of the grinder?

The average angular acceleration of the electric grinder is found using the change in angular velocity over the time it took to stop. This acceleration is negative, indicating a deceleration in the counterclockwise direction.

To calculate the average angular acceleration of the electric grinder, we can use the formula for angular acceleration, which is \

$ \alpha = \frac{\Delta \omega}{\Delta t} $

, where $ \alpha $ is the angular acceleration, $ \Delta \omega $ is the change in angular velocity, and $ \Delta t $ is the change in time.

The grinder is initially spinning at 33 rev/s and takes 89 seconds to come to a stop. Since 1 revolution is $ 2\pi $ radians, the initial angular velocity ($ \omega_i $) is $ 33 \times 2\pi $ rad/s. The final angular velocity ($ \omega_f $) is 0 rad/s since the grinder stops spinning. The change in angular velocity ($ \Delta \omega $) is therefore $ \omega_f - \omega_i = 0 - 33 \times 2\pi $ rad/s. Plugging in the values, we get:

$ \alpha = \frac{0 - (33 \times 2\pi)}{89} $

After calculating this, we find that the average angular acceleration is negative, which indicates a deceleration in the counterclockwise direction (since counterclockwise was defined as positive).