Question

There exists a circular space station with radius 1km where the gravitational pull of the sun and earth cancel. The rotation of the station is in a way that an eart like gravity exists in the ring, which can be considered as a hoop with 1km radius.

1. Find the required constant angular velocity of the station to accomplish this?

2. An astronaut approaches the station with his cylinder craft (radius = 25m, mass=250 kg, length = 300 m), and watches the station. With a compressed gas rocket-thruster mounter on the astronaut's craft, which is tangent to the circular surface halfway thought the length of the ship and can provide up to 4000N of force. How long should the astronaut fire the thruster to match the space stations rotational velocity if he has no initial angular velocity?

Answer 1

1) Let w is the required angular velocity.

radian acceleration, a_rad = R*w^2

g = R*w^2

==> w^2 = g/R

w = sqrt(g/R)

= sqrt(9.8/1000)

= 0.0990 rad/s <<<<<<<<----------------Answer

2) moment of inertia of the cyllinder, I = M*r^2 (since the cyllinder is hollow)

Net torque on the cyllinder, Tnet = I*alfa

F*r*sin(90) = I*(wf - wi)/t

t = I*(wf - wi)/(F*r)

= 250*25^2*(0.099 - 0)/(4000*25)

= 0.155 s 0.0990 rad/s <<<<<<<<----------------Answer

please comment for any clarification.