Question

Engineers are trying to create artificial "gravity" in a ringshaped space station by spinning it like a centrifuge. The ring is 171 m in radius. How quickly must the space station turn in order to give the astronauts inside it apparent weights equal to their real weights at the earth's surface? Use g=9.81 m/s2.

Answer 1

Answer:

The space station must turn at 0.24 rad/s to give the astronauts inside it apparent weights equal to their real weights at the earth’s surface.

Explanation:

In circular motion there’s always a radial acceleration that points toward the center of the circumference, so because the space station is spinning like a centrifuge it has a radial acceleration towards the center of the trajectory. To imitate the weight of the passengers on earth, they should turn the station in a way that the radial acceleration equals earth gravitational acceleration; this is:

$a_{rad}=9.81\frac{m}{s^{2}}\,\,(1)$

And radial acceleration is also defined as:

$a_{rad}=\frac{v^{2}}{R}\,\,(2)$

with v the tangential velocity of the station and R the radius of the ring, solving for v:

$v=\sqrt{a_{rad}R}=\sqrt{(9.81)(171)}\simeq40.96\frac{m}{s^{2}}\,\,(3)$

We can find the angular velocity using the following equation:

$\omega=\frac{v}{R}=\frac{40.96}{171}\simeq0.24\frac{rad}{s}$

That is the angular velocity the space station must turn.