Artificial Gravity: Calculating Centripetal Acceleration

In summary: The answer is that the game is impossible to play if not perfect, but there may be a solution that makes it playable even if not perfect.
  • #1
alfredbester
40
0
Hi,

Question about fictitious force, The set-up is a torus rotating in space of radius r.
First part involves working out the speed of rotation v, for which an artificial gravity of 1g will be created in the torus.
Which is just the centripetal acceleration (centrifugal force?)
For r = 100m at g = 9.81ms-2, v = 31.3 ms-1 (to 3.s.f), w = 0.313 revs s-1. Acting radially outwards.

Next part I'm not sure, we were asked if someone was moving along the corridor (still gravity = g, r = 100m ) at a speed of V = 1ms-1 (in either direction). What will be the magnitude and direction of the acceleration the walker experiences.
I think it's the corolis force, a = 2(V X w) (cross-product), but I'm unsure of the angle between the axis of rotation and the direction the person is walking in.
Any help would be appreciated.
 
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  • #2
first, the velocity vector is along the torus outside rim, perpendicular to the r-vector.
Angular velocity omega is along the axis of the torus, perp to r-vector and v-vector.
Centripetal acceleration vector points toward the center of the torus.

If somebody moves along the rim of the torus, their angular velocity relative to the torus (v=rxw) must be parallel to the angular velocity of the torus itself. so, this is not a coriolus force situation.

But, the moving people's REAL tangential velocity will be 30.3 [m/s] or 32.3 [m/s] at a radius of 100 [m] ... what centripetal accelerations do they need to not sink thru the floor?
 
  • #3
Why not simply consider that the person moving with speed V will experience a force related to v-V or v+V if running opposite or with the toroidal rotation. The force on the runner depends on his velocity.

[itex]\omega[/itex]r = v

Angular acceleration = v2/r or [itex]\omega[/itex] v

useful reference - http://hyperphysics.phy-astr.gsu.edu/hbase/circ.html#rotcon
 
  • #4
Tx, that helps alot.
Also, the question asked about playing table tennis. Assuming the ball is hit @ 30 [m/s] along the corridor. Therefore the centripetal acceleration is a = 37.6 [m/s^2] . This would make the game impossible too play but is there solution that would make the game playable even if not perfect?
 
  • #5
If you start thinking in 3-d, you'll realize that the coriolis force is the same for both players, if they're both right-handed.

Your playing parallel and antiparallel to v_vector is unfair because one player has a = 4g , while the other has a = g/600 .
 

1. What is artificial gravity?

Artificial gravity is a concept in which a simulated gravitational force is created to mimic the effects of gravity on a spacecraft or other artificial environment.

2. How is artificial gravity calculated?

Artificial gravity is calculated using the formula for centripetal acceleration, which is a = v^2/r, where v is the velocity and r is the radius of rotation. This equation determines the acceleration that would be felt by an object moving in a circular path at a constant speed.

3. Why is artificial gravity important for space travel?

Artificial gravity is important for space travel because prolonged exposure to microgravity can have negative effects on the human body, such as muscle atrophy and bone density loss. By creating artificial gravity, astronauts can maintain their health and perform tasks more efficiently.

4. Can artificial gravity be created on Earth?

Yes, artificial gravity can be created on Earth using centrifuges or rotating chambers. However, the effects of artificial gravity on the human body may not be exactly the same as natural gravity, and more research is needed in this area.

5. Are there any risks associated with artificial gravity?

There are some risks associated with artificial gravity, such as motion sickness and disorientation due to the constant rotation. There may also be technical challenges in designing and maintaining artificial gravity systems in space. However, with proper precautions and research, these risks can be minimized.

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