A space station is designed to be operated outside of the Earth\'s gravitational

Question

A space station is designed to be operated outside of the Earth's gravitational field. The structure is given a rotation from rest to a speed "omega" which will simulate the effect of Earth's gravity, g = 9.81m/s^2, (centripetal acceleration) in the crew quarters located 12 m from the axis of rotation. Assume, a uniform rale of increase in angular speed. Calculate, a) the rotational speed (omega), reporting your result in revolutions per minutes, b) the angular acceleration, c) the tangential acceleration, d) the net force (Magnitude and direction) being exerted on a crew of 60 kg mass in one of the quarters at the instance of the structure reaching the speed "omega".

Explanation / Answer

centripetal acceleration a = r*w^2

9.81 = 12*w^2

w = 0.904 rad/s

w = 0.904*60/(2pi)

w = 8.63 revolutions per minute

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b)

angular acceleration alpha = dw/dt = 0

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d)

net force = m*a = 60*9.81 = 588.6 N

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