Two identical flywheels with radius 1.00 m are fixed in place on a table and spinning side-by-side, each spinning about their center as shown. Wheel A is initially spinning in the clockwise direction, and has initial angular velocity of wao = -16.0 rad/s, with 010 = 0 rad, and a constant angular acceleration a = 1.90 rad/s². Wheel B is initially spinning in the counter-clockwise direction, and has initial angular velocity Wgo = 16 rad/s, with 0g0 = 0 rad, and has angular acceleration a = –1.85 rad/s² – 5.33t rad/s³ + 1.02t² rad/s*. string А в sensor sensor sensor sensor . Each wheel has a sensor attached to its perimeter that beeps each time it passes a corresponding sensor attached to the table as shown. The pair of sensor begins aligned when the clock starts and will not beep until the next time they are aligned. How many times has each pair of sensors beeped by the time that both vheels have the same angular velocity for the first time? o. If assume the center of mass of the sensors is 5.00 cm inward from the outer edge of the wheel then vhat is the net translational acceleration acting on the sensor attached to wheel B at t=6.00 s? What angle does this acceleration vector make with the radial direction? . Sketch two graphs. The first graph should be angular acceleration versus time for the two wheel and learly show the time at which the two angular accelerations are equal. The second graph should angular displacement as a function of time for the two wheels and should cover the first ten seconds of motion.

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### Educational Content on Rotational Motion: Analyzing Two Flywheels

#### Introduction

This study involves two identical flywheels of radius 1.00 m fixed on a table, spinning side-by-side. Each wheel spins around its center, but in opposing directions initially.

- **Wheel A**: 
  - Spins clockwise with an initial angular velocity of \( \omega_{A0} = -16.0 \, \text{rad/s} \).
  - Has a constant angular acceleration of \( \alpha_A = 1.90 \, \text{rad/s}^2 \).

- **Wheel B**: 
  - Spins counter-clockwise with an initial angular velocity of \( \omega_{B0} = 16 \, \text{rad/s} \).
  - Has an angular acceleration described by \( \alpha_B = -1.85 \, \text{rad/s}^2 - 5.33t \, \text{rad/s}^3 + 1.02t^2 \, \text{rad/s}^4 \).

#### Diagram Explanation

The diagram includes:

- **Wheel A and Wheel B**: Each wheel has a sensor on its perimeter.
- **Sensors**: Attached to the perimeter which beep when aligned with a corresponding fixed sensor on the table.
- **String and Rotation Direction**: The wheels are depicted with arrows indicating their current direction of rotation. A string is used to suggest the mechanism of torque.

#### Questions and Tasks

a. **Sensor Alignment and Angular Velocity:**

   Determine how often the sensors on each wheel align from the start until both wheels achieve the same angular velocity for the first time. Analyze the relative motion of the wheels for calculations.

b. **Net Translational Acceleration:**

   If the center of mass of the sensors is 5.00 cm inward from the wheel's edge, compute the net translational acceleration on Wheel B's sensor at \( t = 6.00 \) s. Also, determine the angle this acceleration vector forms with the radial direction.

c. **Graph Sketching Tasks:**

   - **Graph 1**: Plot angular acceleration versus time for both wheels. Highlight where the angular accelerations are equal.
   - **Graph 2**: Plot angular displacement over the first ten seconds for each wheel.

#### Analysis Steps

1. **Angular Velocity Calculation:**
   \[
   \omega
Transcribed Image Text:### Educational Content on Rotational Motion: Analyzing Two Flywheels #### Introduction This study involves two identical flywheels of radius 1.00 m fixed on a table, spinning side-by-side. Each wheel spins around its center, but in opposing directions initially. - **Wheel A**: - Spins clockwise with an initial angular velocity of \( \omega_{A0} = -16.0 \, \text{rad/s} \). - Has a constant angular acceleration of \( \alpha_A = 1.90 \, \text{rad/s}^2 \). - **Wheel B**: - Spins counter-clockwise with an initial angular velocity of \( \omega_{B0} = 16 \, \text{rad/s} \). - Has an angular acceleration described by \( \alpha_B = -1.85 \, \text{rad/s}^2 - 5.33t \, \text{rad/s}^3 + 1.02t^2 \, \text{rad/s}^4 \). #### Diagram Explanation The diagram includes: - **Wheel A and Wheel B**: Each wheel has a sensor on its perimeter. - **Sensors**: Attached to the perimeter which beep when aligned with a corresponding fixed sensor on the table. - **String and Rotation Direction**: The wheels are depicted with arrows indicating their current direction of rotation. A string is used to suggest the mechanism of torque. #### Questions and Tasks a. **Sensor Alignment and Angular Velocity:** Determine how often the sensors on each wheel align from the start until both wheels achieve the same angular velocity for the first time. Analyze the relative motion of the wheels for calculations. b. **Net Translational Acceleration:** If the center of mass of the sensors is 5.00 cm inward from the wheel's edge, compute the net translational acceleration on Wheel B's sensor at \( t = 6.00 \) s. Also, determine the angle this acceleration vector forms with the radial direction. c. **Graph Sketching Tasks:** - **Graph 1**: Plot angular acceleration versus time for both wheels. Highlight where the angular accelerations are equal. - **Graph 2**: Plot angular displacement over the first ten seconds for each wheel. #### Analysis Steps 1. **Angular Velocity Calculation:** \[ \omega
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