What Happens to Apparent Gravity in a Rotating Cylindrical Space Station?

AI Thread Summary
In a discussion about a rotating cylindrical space station, participants explore the effects of apparent gravity on an astronaut climbing a spoke to the center. The first question addresses the fractional change in apparent gravity, with a solution suggesting a ratio of 1 + m/M, raising questions about the conservation of angular momentum versus energy. The second question involves calculating where the astronaut lands after letting go halfway up the spoke, with confusion about the conservation principles at play. Participants agree that angular momentum is conserved during the astronaut's descent, while energy may not be due to factors like friction and the station's flexing. The conversation highlights the complexities of physics in a rotating system and the nuances of conservation laws.
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1. Homework Statement

cylindrical space station - large diameter, thin walled - radius r, mass M rotating in deep space, no gravity

1)radial spokes of negligible mass connect the cylinder ti the centre of motion. Astronaut mass m climbs a spoke to the centre. What is the fractional change in apparent gravity on the surface of the cylinder?

2)if the astronaut climbs halfway up a spoke and let's go, how far form the base of the spoke will he hit the cylinder? Assume the astronaut is point like..

2. Homework Equations



3. The Attempt at a Solution

1) Got the answer to be 1+m/M for ratio after/before..

is this right? I applied conservation of energy rather than angular momentum...why is angular momentum not conserved?

2) How do i do this one? Consv of energy again?
 
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anyone?
 
what is conserved as the astronaut climbs down a spoke - angular momentum or total energy, and why?
 
bon said:
what is conserved as the astronaut climbs down a spoke - angular momentum or total energy, and why?
What do you think? (and why?)
 
My hunch is that angular momentum is conserved but not energy...because as he goes down the spoke there is no torque wrt centre of the cylinder..

but can't see why energy wouldn't be conserved..
 
Friction? Heat? Flexing of the space station? (not to mention the motion of the astronaut's body)

Your hunch is correct.
 
diazona said:
Friction? Heat? Flexing of the space station? (not to mention the motion of the astronaut's body)

Your hunch is correct.

Thanks okay so how do I solve part 2?

My attempt:

When he's half way up a spoke, I = Mr^2 + 1/4 mr^2

After he let's go I = Mr^2

angular mom is conserved again so Mr^2 w2 = (Mr^2 + 1/4mr^2)w1...

don't see how i can use this to work out how far from the base of the spoke he hits the cylinder!
 
I don't think I even understand why he'd fall! I thought you only experienced the "apparent" gravity when you were on the inner surface of this rotating cylinder..
 
so...?
 
  • #10
diazona said:
Friction? Heat? Flexing of the space station? (not to mention the motion of the astronaut's body)

Your hunch is correct.

Sorry just thought I'd quote you to see if you can help with my next question... thanks
 
  • #11
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