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

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.

Step-by-step 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(m)/(s^(2))\,\,(1)`

And radial acceleration is also defined as:

`a_(rad)=(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}=√((9.81)(171))\simeq40.96(m)/(s^(2))\,\,(3)`

We can find the angular velocity using the following equation:

`\omega=(v)/(R)=(40.96)/(171)\simeq0.24(rad)/(s)`

That is the angular velocity the space station must turn.