Question

A space station, in the form of a wheel 120 m in diameter, rotates to provide an artificial gravity of 3.00 m/s2 for persons who walk around the inner wall of the outer rim. Find the rate of rotation of the wheel (in revolutions per minute) that will produce this effect

Answer 1

Explanation:

Standing on the inner surface of the rim, and moving with it, each person will feel a normal force exerted by the rim. This inward force causes the 3.00m/s

2

centripetal acceleration,

a

C

=v

2

/r so, v=

a

c

r

=

(3.00m/s

2

)(60.0m)

=13.4m/s

The period of rotation comes from v=

T

2πr

T=

v

2πr

=

13.4m/s

2π(60.0m)

=28.1s

so the frequency of rotation is

f=

T

1

=

28.1s

1

=(

28.1s

1

)(

1min

60s

)=2.14rev/min