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**1. Homework Statement**

A space ship is located in a gravity free region of space. It consists of a large diameter, thin walled cylinder which is rotating freely. It is spinning at a speed such that the apparant gravity on the inner surface is the same as that on earth. The cylinder is of radius r and mass M.

(a) discuss the minimum total work which had to be done to get the cylinder spinning.

(b) radial spokes of negligible mass, connect the cylinder to the centre of rotation. An astronaught of mass m cllimbs a spoke to the centre. What will the fractional change in the appearant gravity on the surface of the cylinder?

(c)If the astronaught climbs halfway up a spoke and lets go how far from the base of the spoke will he hit the cylinder, assuming the astronaught is point-like?

**2. Homework Equations**

omega.r=0 so that means all the normal equations simplify out nicely.

**3. The Attempt at a Solution**

I'm doing this question for revision, so since no answers are provided I'd be grateful if someone could check my answers for (a) and (b):

for (a): I used acceleration as a function of angular velocity and kinetic energy as a function of moment of inertia and angular velocity to get:

ke=0.25Mgr

for (b) using conservation of angluar momentum:

sorry for the mess, I couldn't get latex to come out right (I'll head off to read the introduction angain now!):

a/a0 = (1+m/M)^2

where a0 is original acceleration

I'm not really sure how to start with part (c), so if someone could give me an idea how to start that would be nice.

Thanks

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