A rotating space ship has a mass of 1,000,000 kg, most of it due to a large cyli

Question

A rotating space ship has a mass of 1,000,000 kg, most

of it due to a large cylindrical tank of water (radius 10 m)

on the central axis of the ship (with outer hull radius

20 m). While making its way to Alpha Centauri, the ship

spins about this axis to generate the illusion of gravity.

(a) Initially the rotation rate is set so that the centripetal acceleration of a person just inside the

outer hull is equal to the normal acceleration of

gravity on the surface of the Earth. What is the linear speed of a point just inside the outer hull?

(b) What is the angular velocity of a point just inside

the outer hull?

(c) What is the angular momentum of the ship (For

this part, ignore the mass of the ship outside the

water tanks.)

(d) A year or so into the trip they realize that the rotation is making the pilots seasick. Not wanting to

waste fuel using rockets to slow the rotation, they

decide to use angular momentum to their advantage, and instead pump the water out of the central

tanks into a thin shell around the outer hull. What

is the new angular velocity after this operation?

(Again, consider only the mass of the water.)

(e) What is the acceleration of a person just inside the

outer hull after the operation in part (d)?

Explanation / Answer

a) g = v^2/r

=> v = sqrt(gr) = sqrt(9.8*20) = 14 m/sec answer

b) w = v/r = 14/20 = 0.7 rad/sec answer

c) angular momentum = Iw = mr^2/2 *w = (1000000*10*10/2)*0.7 = 35000000 km.m^2.rad/sec answer

d)conserving angular momentum:

Iw = I'w'

=> 35000000 = mr^2*w'

=> 35000000 = 1000000*20*20*w'

=> w' = 0.0875 rad/sec answer

e) a = rw'^2 = 20*0.0875*0.0875 = 0.153125 m/sec^2 answer

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