Question

You want to design a large, permanent space station so that no artificial gravity is necessary. You decide to shape it like a large coffee can of radius 236 m and rotate it about its central axis. What rotational speed would be required to simulate gravity? The acceleration of gravity is 9.8 m/s². Answer in units of rad/s.

Answer 1

The rotational speed required to simulate gravity on a space station with a radius of 236 meters is approximately 0.204 radians per second.

Step-by-step explanation:

To simulate gravity on a space station shaped like a large coffee can with a radius of 236 meters, we need to determine the rotational speed required to create a centripetal acceleration equal to Earth's gravitational acceleration of 9.8 m/s². The formula for centripetal acceleration (a) is a = ω²r, where ω is the angular velocity in radians per second (rad/s) and r is the radius in meters. To solve for the angular velocity (ω), we set the centripetal acceleration equal to the gravitational acceleration (9.8 m/s²) and solve for ω as follows:

a = ω²r

9.8 m/s² = ω² (236 m)

ω² = 9.8 m/s² / 236 m

ω = √(9.8 m/s² / 236 m)

ω ≈ 0.204 rad/s

The rotational speed required to simulate gravity on the space station would be approximately 0.204 rad/s.