In the video game Halo, a rigid ring of material rotates about a star. The rotational speed of the ring is 3.00 104 m/s, and its radius is 3.05 108 m.

Question

(a) Find the centripetal acceleration of the inhabitants.

 

*notice that this value is less than the acceleration experienced on Earth. This explains the "floatiness" experienced when your character jumps in the game.

(b) The inhabitants of this halo live on the starlit inner surface of the ring and experience a normal contact force n. Acting alone, this normal force would produce an inward acceleration of 1.62 m/s². Additionally, the star at the center of the halo exerts a gravitational force on the ring and its inhabitants. The difference between the total acceleration and the acceleration provided by the normal force is due to the gravitational attraction of the central star. Find the mass of the star.

Answer 1

a) Centripetal (total) acceleration a = v²/r.

b) Gravitational attraction = difference between the total acceleration v²/r and the acceleration n/m provided by the normal force = v²/r – n/m = GM/r², where M is the star mass.