Question

A space station (m = 5.0 x 105 kg) is constructed in the shape of a wheel 22 m in diameter, with
essentially all of its mass at the rim. Once the space station is completed, it is set rotating at a rate such that an object at
the rim experiences a radial/centripetal acceleration equal to the Earth's gravitational acceleration g, thus simulating
Earth's gravity.
A. What must the angular velocity be in order to accomplish this?
B. To get the space station spinning, two small rockets are attached on opposite sides of the rim, each able to
provide a 100 N force tangential to the rim of the station. How long will it take these rockets to reach the
desired rotation rate?

Answer 1

given

diameter d = 22 m

R = d/2 =

22 / 2 = 11 m

M = 5 x 10⁵ kg

F = 100 N

A )

using equation

2 x F x R = I x

2 F R = M R²

2 x 100 x 11 = 5 x 10⁵ x 11² x

= 2 x 100 x 11 / 5 x 10⁵ x 11²

= 3.64 x 10^-5 rad/s²

g = 9.8 m/s²

= angular speed

using now

g = R ²

9.8 = 11 x ²

the angular velocity be in order to accomplish this is = 0.944 rad/s.

B )

the initial angular speed _o = 0 rad/s

we have relation

= _o + t

0.944 = 0 + 3.64 x 10^-5 x t

t = 0.944 / 3.64 x 10^-5

t = 2.6 x 10⁴ sec it will take these rockets to reach the desired rotation rate.