A space station is to provide artificial gravity to support long-term stay of as

Question

A space station is to provide artificial gravity to support long-term stay of astronauts and cosmonauts. It is designed as a large wheel, with all the compartments in the rim, which is to rotate at a speed that will provide an acceleration similar to that of terrestrial gravity for the astronauts (their feet will be on the inside of the outer wall of the space station and their heads will be pointing toward the hub). After the space station is assembled in orbit, its rotation will be started by the firing of a rocket motor fixed to the outer rim, which fires tangentially to the rim. The radius of the space station is R = 58.1 m, and the mass is M = 4.67

Explanation / Answer

When the Ring in the space ship is rotating, Each Mass will feel a centrifugal force

F = Mv^2/R

this force must equal to their gravitational weight

Mv^2/r = mg

v^2/r = g

v = sqrt(gr) = sqrt(9.8 X 58.1) = 23.86 m/s

For this the ring must have an angular velocity w = v/r

w = 23.86/58.1 = 0.4107 rad/s

The moment of Inertia of the ring = Mr^2 = 4.67X10^5 X 58.1^2 = 1.576X10^9

Torque due to rocket = FXr = 175 x 58.1 = 10167.5 Nm

Angular acceleration = Torque/ I = 10167.5/(1.576X10^9) = 6.45X10^-6

Time take to reach required w = W/angular acceleration

time = 0.4107/(6.45X10^-6) = 63660 s = 17 hrs 41 mins

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