Question

Is the energy of a rotating cylindrical spacecraft conserved when a point-like astronaut climbs up a spoke connecting the walls with the center of the cylinder?
If so, when I calculate the fractional change in apparent gravity at the walls when the astronaut reaches the middle I get different answers using conservation of angular momentum and conservation of energy

Answer 1

Apparent gravity \[g'=r \omega ^{2}\]
Consv. of energy:
\[\frac{ 1 }{ 2 } (M+m) r ^{2} \omega ^{2}=\frac{ 1 }{ 2 } M r ^{2} \omega ^{2}\]
Consv. of L:
\[ (M+m) r ^{2} \omega= M r ^{2} \omega\]

The first one gives \[\frac{ g-g' }{ g }=\frac{ m }{ M }\]
The second one: \[\frac{ g-g' }{ g }=\frac{ m ^{2} }{ M ^{2} }+\frac{ 2m }{ M }\]
If i did them right of course