This graph shows the angular velocity of a turntable as a function of time.What is its average angular acceleration between t = 2 s and t = 4 s? A)−10 rad/s² B)−5 rad/s² C)0 rad/s² D)5 rad/s² E)10 rad/s²

Question

Quizplus · Accepted Answer

The average angular acceleration is given by the change in angular velocity divided by the time interval:

$$	ext{Average Angular Acceleration} = \frac{\Delta\omega}{\Delta t}$$

Between $t=2$ s and $t=4$ s, the change in angular velocity is the final angular velocity minus the initial angular velocity:

$$\Delta\omega = \omega_f - \omega_i$$

From the graph, we can see that the initial angular velocity at $t=2$ s is $\omega_i = 10$ rad/s and the final angular velocity at $t=4$ s is $\omega_f = 0$ rad/s. Thus,

$$\Delta\omega = \omega_f - \omega_i = 0 - 10 = -10 	ext{ rad/s}$$

The time interval is $\Delta t = 4 - 2 = 2$ s. Thus,

$$	ext{Average Angular Acceleration} = \frac{\Delta\omega}{\Delta t} = \frac{-10}{2} = \boxed{	extbf{(B) }-5 	ext{ rad/s}^2}$$

This Graph Shows the Angular Velocity of a Turntable as a Function