Problem 9.2 Classical Mechanics: Astronaut in a rotating space station

Click For Summary
SUMMARY

The discussion centers on the acceleration experienced by an astronaut in a rotating space station, specifically addressing the forces acting in a rotating frame of reference. The key equations involved include Newton's second law for a rotating frame: mr'' = F net + Fcor + Fcf, where Fnet represents centripetal acceleration (ma_c), Fcor is the Coriolis force (2m(r'xΩ)), and Fcf is the centrifugal force (m(Ωxr)xΩ). The confusion arises from the perception of centrifugal force as the sole force acting on the astronaut, despite the presence of Coriolis and centrifugal forces in the equations. The astronaut, in a non-inertial frame, perceives no motion, leading to the conclusion that if at rest, both r'' and r' equal zero, nullifying the Coriolis force.

PREREQUISITES
  • Understanding of Newton's laws of motion
  • Familiarity with rotational dynamics
  • Knowledge of non-inertial reference frames
  • Basic concepts of centripetal and centrifugal forces
NEXT STEPS
  • Study the implications of non-inertial frames in classical mechanics
  • Learn about the Coriolis effect and its applications
  • Explore advanced topics in rotational dynamics
  • Review examples of forces in rotating systems, such as satellites
USEFUL FOR

Students of physics, particularly those studying classical mechanics, as well as educators and anyone interested in the dynamics of rotating systems and non-inertial reference frames.

SebastianRM
Messages
39
Reaction score
4

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.
 
Last edited by a moderator:
Physics news on Phys.org
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.
 
  • Like
Likes SebastianRM
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

Similar threads

  • · Replies 1 ·
Replies
1
Views
2K
Replies
1
Views
4K
  • · Replies 20 ·
Replies
20
Views
2K
  • · Replies 7 ·
Replies
7
Views
3K
  • · Replies 14 ·
Replies
14
Views
22K
  • · Replies 38 ·
2
Replies
38
Views
4K
Replies
1
Views
3K
  • · Replies 1 ·
Replies
1
Views
8K
  • · Replies 12 ·
Replies
12
Views
5K
  • · Replies 1 ·
Replies
1
Views
3K