a space station is designed to rotate about it central axis in order to stimulat

Question

a space station is designed to rotate about it central axis in order to stimulate gravity for any astronauts onboard. we can approximate the station as a thin hoop with a mass m=5000 kg, diameter D=80 m and ordinarily it rotates at a rate of Wo= 0.49 rad/s. however, the station was damaged and spins instead at a rate of w=1 rad/s. to correct this you must attatch yourself to the outside edge of the space station and use your space suit thrusters to exert a torque to slow the rotation. take your mass to be 50 kg.

a) determine the angular deceleration a if slowing the station to w= 0.49 rad/s takes 60 seconds?

b) determine the force you must apply to produce the torque necessary for this deceleration?

c) what was the artificial gravitational aceleration while the station was rotating at 1 rad/s?

Explanation / Answer

a)

w2=w1+a t

a = (1-0.49) / 60

angular deceleration ,a = 0.0085 m/s2

b)

Torque, T = I * angular acceleration

F*r = I * angular acceleration

here it is a thin hoop, so I = mr^2

F*r= m*r^2* angular acceleration

F = m*r*angular acceleration

F = 5050*40*0.0085

F = 1717 N

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