Artificial Gravity in Space

In the movie 2001 A Space Odyssey, the acceleration caused by gravity is replaced with centripetal acceleration to simulate gravity in space. In the movie, a space ship contains a rotating wheel which rotates at a uniform speed. People and objects on the edge of this wheel experience a normal force from the edge of the wheel which is equal to the normal force they would experience from gravity.

In the picture above, we can estimate the radius of the ship to be 10 meters. We can find the tangential speed at which the circumference of the ship should be rotating by setting mass x gravity equal to velocity squared over radius times mass. We can cancel out mass, and if we know the radius and we know gravity we can then solve to find how fast the ship would need to be rotating.

Interestingly, if someone was at the center of the wheel they would be weightless since radius would be equal to zero. If they moved halfway down the ladder, the radius would be half of the total radius of the ship, and thus if we plug this into our equation (a = v^2/r) we find that artificial gravity would be half of gravity on earth.

One may ask why the current space station did not follow this design, considering that muscle loss due to weightlessness is an issue for astronauts. The answer is that the current space station had to be built in small parts, and a wheel would not be able to create artificial gravity until it was fully completed. Thus, a rotating wheel was impractical.