3. A person (treated as a red point object) of mass m₁ a rod of length L counterclockwise W m2 50 kg is attached to = : 1 m and mass M = 20 kg. Together, they are rotating around a pivot (green), with angular speed w = 2 rad/s: M, L vo = = m1 5 kg is thrown with speed A ball (purple point object) of mass m₂ Vo = 30 m/s at the person, who catches the ball just as the bar is oriented horizontally during its rotation (as seen in the figure). If the bar and person are stationary after the catch, how far away from the pivot was the ball thrown (that is, what is the length of the dashed black line)? Hint: Use the conservation of angular momentum.
3. A person (treated as a red point object) of mass m₁ a rod of length L counterclockwise W m2 50 kg is attached to = : 1 m and mass M = 20 kg. Together, they are rotating around a pivot (green), with angular speed w = 2 rad/s: M, L vo = = m1 5 kg is thrown with speed A ball (purple point object) of mass m₂ Vo = 30 m/s at the person, who catches the ball just as the bar is oriented horizontally during its rotation (as seen in the figure). If the bar and person are stationary after the catch, how far away from the pivot was the ball thrown (that is, what is the length of the dashed black line)? Hint: Use the conservation of angular momentum.
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Transcribed Image Text:**Title: Angular Momentum Conservation Problem**
**Physics Problem: Rotational Motion and Angular Momentum**
**Problem Statement:**
A person (treated as a red point object) of mass \( m_1 = 50 \, \text{kg} \) is attached to a rod of length \( L = 1 \, \text{m} \) and mass \( M = 20 \, \text{kg} \). Together, they are rotating counterclockwise around a pivot (green), with angular speed \( \omega = 2 \, \text{rad/s} \):
**Diagram Explanation:**
- The rod is depicted as a horizontal blue line with length \( L \) and mass \( M \), pivoting around a green point.
- The person is represented as a red point \( m_1 \) at the end of the rod.
- Angular speed \( \omega \) is indicated with a green curved arrow pointing counterclockwise.
**Additional Scenario:**
A ball (purple point object) of mass \( m_2 = 5 \, \text{kg} \) is thrown with speed \( v_0 = 30 \, \text{m/s} \) at the person. The person catches the ball just as the bar is oriented horizontally during its rotation (as seen in the figure).
If the bar and person are stationary after the catch, how far away from the pivot was the ball thrown (that is, what is the length of the dashed black line)?
**Hint: Use the conservation of angular momentum.**
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**Educational Objective:**
This problem is designed to help students understand and apply the conservation of angular momentum in a rotational system.
**Key Concepts:**
- Conservation of Angular Momentum
- Rotational Motion
- Linear to Angular Conversion
**Steps to Solution:**
1. Calculate the initial angular momentum of the system (person + rod).
2. Determine the angular momentum of the ball relative to the pivot before the catch.
3. Apply the conservation of angular momentum to find the distance from the pivot where the ball was thrown.
**Solution Highlights:**
- Initial angular momentum of the system (person and rod).
- Calculation involving the mass, velocity, and distance of the thrown ball.
- Conservation equation setup and solving for the distance.
This problem integrates concepts from linear and rotational dynamics, providing a comprehensive understanding of angular momentum conservation in real-world scenarios.
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