[LO 25.1, 21.4] Two astronauts (figure), each having a mass of 70 kg, are connected by a d = 14-m rope of negligible mass. They are isolated in space, orbiting their center of mass at speeds of 3.8 m/s. By pulling on the rope, one astronaut shortens the distance between them by half to 7 m. What is the new angular momentum of the system? ( in units of kg m^2/s )

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**Angular Momentum of a Two-Astronaut System**

Two astronauts, each with a mass of 70 kg, are connected by a 14-meter rope of negligible mass. They are isolated in space, orbiting their center of mass at a speed of 3.8 m/s. One astronaut pulls on the rope, shortening the distance between them to 7 meters. We need to find the new angular momentum of the system.

**Diagram Explanation:**

- The image shows two astronauts in space connected by a rope.
- Each astronaut is represented wearing a spacesuit with arrows indicating their direction of motion.
- The center of mass (CM) is marked with an "X" between them.
- The original distance \(d\) between the astronauts is 14 meters, which is reduced to 7 meters by one of the astronauts pulling on the rope.
- Arrows indicate the rotational movement around the center of mass.

**Objective:**

Calculate the new angular momentum of the system, expressed in \( \text{kg} \cdot \text{m}^2/\text{s} \).
Transcribed Image Text:**Angular Momentum of a Two-Astronaut System** Two astronauts, each with a mass of 70 kg, are connected by a 14-meter rope of negligible mass. They are isolated in space, orbiting their center of mass at a speed of 3.8 m/s. One astronaut pulls on the rope, shortening the distance between them to 7 meters. We need to find the new angular momentum of the system. **Diagram Explanation:** - The image shows two astronauts in space connected by a rope. - Each astronaut is represented wearing a spacesuit with arrows indicating their direction of motion. - The center of mass (CM) is marked with an "X" between them. - The original distance \(d\) between the astronauts is 14 meters, which is reduced to 7 meters by one of the astronauts pulling on the rope. - Arrows indicate the rotational movement around the center of mass. **Objective:** Calculate the new angular momentum of the system, expressed in \( \text{kg} \cdot \text{m}^2/\text{s} \).
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