Physics
posted by Malcom on .
A team is chosen to design an orbiting space station that is shaped like a wheel 5o meters in diameter with is mass of 4*10^5 kg contained in the rim portion of the wheel. The space station will rotate at a rate such that a person working in the wheel will experience a simulated gravitational force equal to that of earth, meaning that the normal force of the floor on an a person will be equal to g=9.8m/s^2. When the station is finished, it will have to be set at a required rotation rate to produce this “artificial gravity”. This is accomplished with the firing of four small thruster rockets attached symmetrically to the outer wall of the wheel. The rockets will fire for 1 hour to bring the staion “up to speed”. I have to determine the thrust, or force, each rocket must have to produce the required rate in this particular amount of time. Assume the station starts rotating from rest.
Where to start?

You want the space statiion to rotate at angular rate w such that
R w^2 = g, where R = 25 m.
Therefore w = sqrt(g/R).
Treat the space station as a wheel with all of its mass at distance R from the center. Its moment of inertia wil them be
I = M R^2
The "torque impulse" applied by the rockets in 1 hour must be enough to provide the required angular momentum of the space station, which is I w.
4 T R *(3600 s) = I w = M R^2 w
Solve for the thrust, T. The number 4 comes from the number of thrusters