Problem 9.2 Classical Mechanics: Astronaut in a rotating space station

In summary: Therefore the only force acting on the astronaut is the centrifugal force, which is equal to ##m\textbf{r}\times\Omega\times\Omega##. This force is directed away from the center of rotation and is responsible for the feeling of being pushed away. In summary, the astronaut in a rotating space station experiences only the centrifugal force, which pushes them away from the center of rotation.
  • #1
SebastianRM
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Homework Statement


Acceleration experienced by an astronaut in a rotating space station.

Homework Equations


What force would he experience is his own rotating frame of reference.

The Attempt at a Solution


Newton's second Law for a rotating frame is:
mr'' = F net+ Fcor + Fcf
Fnet (In the innertial frame) = ma_c (centripetal acc)
Fcor = 2m(r'xΩ)
Fcf = m(Ωxr)xΩ

I saw online that the answer was just the centrifugal force since the astronaut feels like he is being pushed away. However I do not understand why is it only that one and not Fcor + Fcf , so I am confused on how to understand the motion. From his view, he is not moving (the station wall is pushing back on him) which I would think of that to be Fnet , but if he isn't moving in the rotational frame so what is the acceleration r'' describing.
 
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  • #2
SebastianRM said:

Homework Statement


Acceleration experienced by an astronaut in a rotating space station.

Homework Equations


What force would he experience is his own rotating frame of reference.

The Attempt at a Solution


Newton's second Law for a rotating frame is:
mr'' = F net+ Fcor + Fcf
Fnet (In the innertial frame) = ma_c (centripetal acc)
Fcor = 2m(r'xΩ)
Fcf = m(Ωxr)xΩ

I saw online that the answer was just the centrifugal force since the astronaut feels like he is being pushed away. However I do not understand why is it only that one and not Fcor + Fcf , so I am confused on how to understand the motion. From his view, he is not moving (the station wall is pushing back on him) which I would think of that to be Fnet , but if he isn't moving in the rotational frame so what is the acceleration r'' describing.

If he is at rest then ##\textbf{r}''## ##=0##. Also, since ## \textbf{r}'## ##=0##, the coriolis force is zero.
 
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1. What is the purpose of Problem 9.2 in Classical Mechanics?

Problem 9.2 in Classical Mechanics is designed to help students understand the concept of centripetal force and its application in a rotating frame of reference. It also allows students to practice problem-solving skills using the laws of classical mechanics.

2. What is the scenario described in Problem 9.2?

The problem describes an astronaut inside a rotating space station, experiencing a centripetal force due to the rotation of the station. The astronaut is attached to a rope and is performing a simple pendulum motion, swinging back and forth as the station rotates.

3. What are the key concepts involved in solving Problem 9.2?

The key concepts involved in this problem are centripetal force, Newton's laws of motion, and the concept of a rotating frame of reference. Students will need to apply these concepts to calculate the tension in the rope and the astronaut's velocity and acceleration.

4. How can I approach solving Problem 9.2?

First, draw a free-body diagram to identify all the forces acting on the astronaut. Then, use Newton's laws of motion to set up equations of motion for the astronaut in the rotating frame of reference. Finally, solve the equations to find the unknown quantities.

5. What are some real-world applications of the concepts in Problem 9.2?

The concept of centripetal force and rotating frames of reference are important in understanding the motion of objects in circular motion, such as satellites orbiting the Earth or planets orbiting the sun. It also has applications in engineering, such as designing amusement park rides or analyzing the forces on cars driving around a curved track.

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