The graph shows the angular velocity of a unicycle wheel of radius 0.3 meters as a performer does a trick. Counterclockwise is counted as positive. a. What is the angular acceleration at t = 4 s? b. What is the angular acceleration att = 7 s? c. What is the angular acceleration at t = 9 s? d. Make a plot of angular acceleration versus time for the unicycle wheel. e. What is the change in angle A0 for the ten seconds? Give answer in radians and in rotations. f. How far is the unicycle from the starting point after 10 seconds?

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**Angular Motion of a Unicycle Wheel**

1. The graph shows the angular velocity of a unicycle wheel of radius 0.3 meters as a performer does a trick. Counterclockwise is counted as positive.

   **a.** What is the angular acceleration at \( t = 4 \, \text{s} \)?

   **b.** What is the angular acceleration at \( t = 7 \, \text{s} \)?

   **c.** What is the angular acceleration at \( t = 9 \, \text{s} \)?

   **d.** Make a plot of angular acceleration versus time for the unicycle wheel.

   **e.** What is the change in angle \( \Delta \theta \) for the ten seconds? Give the answer in radians and in rotations.

   **f.** How far is the unicycle from the starting point after 10 seconds?

   **g.** At what time is the wheel furthest from its starting point?

**Graph Analysis**

- **Angular Velocity vs. Time Graph**:
  - X-axis: Time (sec), ranging from 0 to 10 seconds.
  - Y-axis: Angular velocity (rad/sec), ranging from 0 to 2 rad/sec.
  - Observations: The graph shows a line starting at 2 rad/sec at \( t = 0 \), decreasing linearly to -2 rad/sec at \( t = 8 \) seconds, then increasing to 0 rad/sec at \( t = 10 \) seconds.

- **Angular Acceleration vs. Time Graph**:
  - X-axis: Time (sec), ranging from 0 to 10 seconds.
  - Y-axis: Angular acceleration (rad/sec²), ranging from 0 to 1 rad/sec².
  - Note: This plot needs to be created from the rate of change of the angular velocity graph. 

This information provides a comprehensive view for analyzing the unicycle's motion during the trick.
Transcribed Image Text:**Angular Motion of a Unicycle Wheel** 1. The graph shows the angular velocity of a unicycle wheel of radius 0.3 meters as a performer does a trick. Counterclockwise is counted as positive. **a.** What is the angular acceleration at \( t = 4 \, \text{s} \)? **b.** What is the angular acceleration at \( t = 7 \, \text{s} \)? **c.** What is the angular acceleration at \( t = 9 \, \text{s} \)? **d.** Make a plot of angular acceleration versus time for the unicycle wheel. **e.** What is the change in angle \( \Delta \theta \) for the ten seconds? Give the answer in radians and in rotations. **f.** How far is the unicycle from the starting point after 10 seconds? **g.** At what time is the wheel furthest from its starting point? **Graph Analysis** - **Angular Velocity vs. Time Graph**: - X-axis: Time (sec), ranging from 0 to 10 seconds. - Y-axis: Angular velocity (rad/sec), ranging from 0 to 2 rad/sec. - Observations: The graph shows a line starting at 2 rad/sec at \( t = 0 \), decreasing linearly to -2 rad/sec at \( t = 8 \) seconds, then increasing to 0 rad/sec at \( t = 10 \) seconds. - **Angular Acceleration vs. Time Graph**: - X-axis: Time (sec), ranging from 0 to 10 seconds. - Y-axis: Angular acceleration (rad/sec²), ranging from 0 to 1 rad/sec². - Note: This plot needs to be created from the rate of change of the angular velocity graph. This information provides a comprehensive view for analyzing the unicycle's motion during the trick.
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