The graph below shows a plot of angular acceleration in rad/s2 versus time from t = 0 s to t = 8 s. The change in angular velocity, $\Delta$$ \omega $, during this 8-second period is:
A) $18 \frac{\mathrm{rad}}{\mathrm{~s}}$ , CW.
B) $18 \frac{\mathrm{rad}}{\mathrm{~s}}$ , CCW.
C) $23 \frac{\mathrm{rad}}{\mathrm{~s}}$ , CW.
D) $23 \frac{\mathrm{rad}}{\mathrm{~s}}$ , CCW.
E) $31 \frac{\mathrm{rad}}{\mathrm{~s}}$ , CW.

Question

The graph below shows a plot of angular acceleration in rad/s2 versus time from t = 0 s to t = 8 s. The change in angular velocity, $\Delta$$ \omega $, during this 8-second period is: 
A) $18 \frac{\mathrm{rad}}{\mathrm{~s}}$ , CW. 
B) $18 \frac{\mathrm{rad}}{\mathrm{~s}}$ , CCW. 
C) $23 \frac{\mathrm{rad}}{\mathrm{~s}}$ , CW. 
D) $23 \frac{\mathrm{rad}}{\mathrm{~s}}$ , CCW. 
E) $31 \frac{\mathrm{rad}}{\mathrm{~s}}$ , CW.

Quizplus · Accepted Answer

The change in angular velocity is equal to the area under the graph of angular acceleration versus time. Looking at the graph, we can see that the area under the curve is positive and relatively large, indicating a significant change in angular velocity. Since the angular acceleration is positive for most of the time, the change in angular velocity is in the direction of the angular acceleration, which is clockwise. Therefore, the answer is choice C.

The Graph Below Shows a Plot of Angular Acceleration in Rad/s2