An electric clock is hanging on the wall in the living room. The clock is unplugged, and the second hand comes to a halt over a brief period of time. During this period, what is the direction of the angular acceleration of the second hand?

a. clockwise
b. counterclockwise

Why?

I choose clockwise but I am not sure why. Please help!

angular acceleration= wf-wi/time

Notice that wf is zero, so if clockwise is positive, then angular acceleration is the negative of that.

Answer is Counter Clock Wise

Since the clock is unplugged and the second hand comes to a halt, we can assume that the initial angular velocity (wi) of the second hand is not zero, but its final angular velocity (wf) becomes zero over the brief period of time.

In this case, the angular acceleration can be calculated as:
angular acceleration = (wf - wi) / time

Given that wf is zero and the second hand stops moving, the final angular velocity is zero. Therefore, the formula becomes:
angular acceleration = (0 - wi) / time
angular acceleration = - wi / time

If we consider clockwise as the positive direction, then the angular acceleration will be negative (clockwise), since wi is in the counterclockwise direction. Hence, the correct answer is:
a. clockwise

So, the angular acceleration of the second hand is clockwise.

To determine the direction of the angular acceleration of the second hand of the electric clock, let's consider the concept of angular acceleration and the given scenario.

Angular acceleration (α) is the rate of change of angular velocity (ω) over time (t), as described by the formula α = (ωf - ωi) / t, where ωf is the final angular velocity, ωi is the initial angular velocity, and t is the amount of time.

In the given scenario, the clock is unplugged, and the second hand comes to a halt over a brief period of time. This implies that the final angular velocity (ωf) of the second hand is zero, as it has stopped moving. The initial angular velocity (ωi) is also zero, as the clock is unplugged and not moving.

Therefore, using the formula for angular acceleration α = (ωf - ωi) / t, we have α = (0 - 0) / t = 0 / t = 0.

Since the angular acceleration is zero, it means that there is no change in angular velocity during the brief period. As such, the second hand does not experience any angular acceleration, and it remains stationary.

Therefore, the correct answer is: The direction of the angular acceleration of the second hand is neither clockwise nor counterclockwise since there is no angular acceleration happening when the clock is unplugged and the second hand is stationary.