Question

In order to produce artificial gravity, a large cylindrical space station is spinning in space. If the radius of the space station is 70 m, with what angular velocity should the space station spin in order to provide a gravitational acceleration for the occupants of 9.81m/s^2? If the mass of the space station is 60 tonnes, what is the kinetic energy of the spinning space station?

A) Angular velocity = 0.1rad/s, Kinetic energy = 2.205×10^7J
B) Angular velocity =0.2rad/s, Kinetic energy = 4.41×10^7J
C) Angular velocity = 0.3 rads, Kinetic energy = 6.615×10^7J
D) Angular velocity = 0.4rad/s, Kinetic energy = 8.82×10^7J

Answer 1

The angular velocity needed to produce an artificial gravity of 9.81 m/s² is 0.3 rad/s. The kinetic energy of the spinning space station is 6.615 × 10^7 J.

Step-by-step explanation:

To calculate the angular velocity needed to produce an artificial gravity of 9.81 m/s², you can use the formula a = ω²r, where a is the acceleration, ω is the angular velocity, and r is the radius. Rearranging the formula, you get ω = sqrt(a/r). Plugging in the values for a = 9.81 m/s² and r = 70 m, you get ω = 0.3 rad/s.

To calculate the kinetic energy of the spinning space station, you can use the formula KE = (1/2) I ω², where KE is the kinetic energy, I is the moment of inertia, and ω is the angular velocity. The moment of inertia for a cylindrical space station is 0.5 mR², where R is the radius. Plugging in the values for mass = 60,000 kg, radius = 70 m, and angular velocity = 0.3 rad/s, you get KE = 6.615 × 10^7 J.