Question

A space station is constructed in the shape of a hollow ring of mass 5.00 x10^4 kg. Members of the crew walk on a deck formed by the inner surface of the outer cylindrical wall of the ring, with radius r=100 m. At rest when constructed, the ring is set rotating about its axis so that the people inside experience an effective free-fall acceleration equal to g. (See Fig. P11.29.) The rotation is achieved by firing two small rockets attached tangentially to opposite points on the rim of the ring.

Answer 1

(a) What angular momentum does
the space station acquire?

(b) For what time interval must
the rockets be fired if each exerts a thrust of 125 N?

Answer 2

So first, you'll need to know the moment of inertia of a ring. What is that?

Answer 3

We need to know that because the angular moment is
\[ L = I \omega \]
and hence we need \( I \) and \( \omega \)

Answer 4

I think its I=mr^2

Answer 5

Yes. And what is the angular velocity \( \omega \) in this case?

Answer 6

What you want is the ring to have the velocity required so that a person in the ring feels a centripetal force equal to gravity. In other words,
\[ \frac{v^2}{r} = g \]
Now relate that to \( \omega \). Hint: \( v = \omega r \).

Answer 7

if \( v = \omega r \), then
\[ \frac{v^2}{r} = \omega^2 r. \] Thus if the centripetal acceleration is exactly equal to to \( g \), then
\[ \omega^2 = \frac{g}{r} \]

Hence the angular momentum is
\[ L = I \omega = mr^2 \sqrt{\frac{g}{r}} \]

Answer 8

oh ok I found my mistake. lol

Answer 9

*Stalking you*