A space station is constructed in the shape of a wheel 22 m in diameter, with es

Question

A space station is constructed in the shape of a wheel 22 m in diameter, with essentially all its weight (5.0 Times 10^5 kg) 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 acceleration equal to the Earth's gravitational acceleration g, thus simulating Earth's gravity. To accomplish this, two small rockets are attached on opposite sides of the rim, each able to provide a 100 N force. How long will it take to reach the desired rotation rate and how many revolutions will the space station make in this time? Your answer must he organized, clear, and include the elements of the problem soiling path: Focus the Problem Describe the Physics Plan the Solution Execute and Evaluate

Explanation / Answer

let w is the angular speed required,

a_rad = R*w^2

g = R*w^2

==> w = sqrt(g/R)

= sqrt(9.8/22)

= 0.6674 rad/s

Moment of inertia of wheel, I = M*R^2

= 5*10^5*22^2

= 2.42*10^8 kg.m^2

Torque on the wheel, T = 2*R*F

= 2*22*100

= 4400 N.m

angular acceleration , alfa = T/I

= 4400/(2.42*10^8)

= 1.81818*10^-5 rad/s^2

let t is the time taken.

Apply, w = wo + alfa*t

w = 0 + alfa*t

==> t = w/alfa

= 0.6674/(1.81818*10^-5)

= 36707 s or 10.2 hours

angular dispalcement,

theta = wo*t + 0.5*alfa*t^2

= 0 + 0.5*(1.81818*10^-5)*(36707)^2

= 12249 rad

= 12249/(2*pi)

= 1950 revolustions

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