One problem for humans living in outer space is that they are apparently weightl

Question

One problem for humans living in outer space is that they are apparently weightless. One way around this problem is to design a space station that spins about its center at a constant rate. This creates "artificial gravity" at the outside rim of the station.

Part A

If the diameter of the space station is 800m , how many revolutions per minute are needed for the "artificial gravity" acceleration to be 9.80m/s2?

Part B

If the space station is a waiting area for travelers going to Mars, it might be desirable to simulate the acceleration due to gravity on the Martian surface (3.70m/s2). How many revolutions per minute are needed in this case?

Explanation / Answer

As d = 800 m, r = 400 m.

Thus,

w^2 r = g

--> w = sqrt(g/r)

Thus,

w = 0.1565 rad/s

or

w = 1.49 revolutions/minute   [answer, PART A]

************************

If g = 3.70 m/s^2 instead,

w = sqrt(g/r)

= 0.09618 rad/s

or

= 0.918 revolutions/minute   [ANSWER, PART B]

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