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 Originally Posted by OngBonga
I did think when I watched it that it was a little unrealistic to go the the centre. The closer to the centre you are, the more centrifugal force you experience and the "gravity" is stronger. If the ship is too small, even at the edge the "gravity" your head feels is more than your feet, to the point you would notice. I would imagine this would be very noticeable in the centre.
You have it backwards. The "gravity" is really a centripetal acceleration in this rotating reference frame.
a_cent = -{v_perp}^2 / r
where a_cent is the centripetal acceleration felt by the object, v_perp is the speed of the object perpendicular to the vector r, which points perpendicularly from the axis of rotation to the object.
(bold indicating a vector)
Note the - sign indicates a_cent is in the opposite direction of r, as a_cent points toward the center and r points away from the center.
v_perp is proportional to |r| for an object in circular motion, and always perpendicular to r.
We can derive this from the definition of radians {arc length} = r {theta} if we take the time derivative of both sides.
v_perp = r {omega}
where omega is the angular velocity of the spaceship, and r is the distance from the axis of rotation.
Plugging this in to the first equation above, dropping the - sign and vector notation to talk about the magnitudes of these forces, now.
a_cent = (r {omega})^2 / r = r {omega}^2
We see that for a given omega, increasing r is increasing a_cent, which means we feel that gravity increases with increasing distance from the axis of rotation.
EDIT: we also see that when we move toward the center, we keep decreasing our distance from the axis of rotation. Decreasing r decreases the a_cent, i.e. the strength of the artificial gravity. At the axis of rotation, there is no a_cent, and the artificial gravity is 0 m/s^2 at the axis.
EDIT2: OH FFS!!! Me losing points for rookie mistakes!!! a force is not equal to an acceleration!!! Gah!
Shame on me!!
All those times I talk about F_cent I really meant to say a_cent, the centripetal acceleration.
I am so ashamed. I have corrected my errors.
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