If a circular space station has on outside radius of 750Km, how fast must the space station rotate in order to give an astronaut with a mass of 90Kg an acceleration of 9.8m/s^2?
To calculate the required rotational speed of the circular space station, we can use the centripetal acceleration formula:
ac = v^2 / r
where ac is the centripetal acceleration, v is the linear velocity, and r is the radius.
Given:
Outside radius (r) of the space station = 750 km = 750,000 m
Acceleration (ac) = 9.8 m/s^2 (gravitational constant on Earth)
We need to find the linear velocity (v).
Rearranging the formula, we get:
v = sqrt(ac * r)
Substituting the given values, we find:
v = sqrt(9.8 * 750,000)
Calculating the square root:
v ≈ 8676.78 m/s
Therefore, the space station must rotate at a linear velocity of approximately 8676.78 m/s to provide an astronaut with a mass of 90 kg an acceleration of 9.8 m/s^2.