Okay, doesn't have to be a habitat but just an environment with pseudo gravity caused by contripetal force. And I have a niggling question.
In such an environment, as there is no real gravity, a dropped object will not accelerate towards the floor as it no longer has any forces acting on it (bar a slight force from air resistance and coriolis). However it will still appear to fall towards the floor because without any forces on it, it will continue to travel in the direction it was already moving (no change in velocity). This direction will be at a tangent to the rotation of the habit at the instant it was released. It's just a little difficult to visulaise this but in the diagram I've included object O is 'vertically' above point A at the moment it is released so both O and A are travelling 'horizontally' in the diagram (though at different speeds). As their movement at this instant is exactly parallel O is not moving towards A at all. A short while later (2) O is still moving 'horizontally' but A has continued to rotate so now (at 45 degrees) approximately half of O's velocity component is towards A. Later after A has rotated farther and is now moving vertically all of O's velocity is straight towards A. However it's speed is still constant (ignoring air resistance) so, from the point of view of an observer at A ,the object O has an apparent acceleration towards it. My question is what would this apparent acceleration be? Would it be the same as the pseudo graviational acceleration caused by the rotation?
I'm afraid my maths is just not up to it. I have done a bit of googling but all I could find out is that the object O would appear to fall directly towards A but I couldn't find anything on it's change of relative velocity.
In such an environment, as there is no real gravity, a dropped object will not accelerate towards the floor as it no longer has any forces acting on it (bar a slight force from air resistance and coriolis). However it will still appear to fall towards the floor because without any forces on it, it will continue to travel in the direction it was already moving (no change in velocity). This direction will be at a tangent to the rotation of the habit at the instant it was released. It's just a little difficult to visulaise this but in the diagram I've included object O is 'vertically' above point A at the moment it is released so both O and A are travelling 'horizontally' in the diagram (though at different speeds). As their movement at this instant is exactly parallel O is not moving towards A at all. A short while later (2) O is still moving 'horizontally' but A has continued to rotate so now (at 45 degrees) approximately half of O's velocity component is towards A. Later after A has rotated farther and is now moving vertically all of O's velocity is straight towards A. However it's speed is still constant (ignoring air resistance) so, from the point of view of an observer at A ,the object O has an apparent acceleration towards it. My question is what would this apparent acceleration be? Would it be the same as the pseudo graviational acceleration caused by the rotation?
I'm afraid my maths is just not up to it. I have done a bit of googling but all I could find out is that the object O would appear to fall directly towards A but I couldn't find anything on it's change of relative velocity.
