The figure shows a system of four m = 5.3 kg point masses that rotates at an ang

Question

The figure shows a system of four m = 5.3 kg point masses that rotates at an angular speed of 5 rev/s. The masses are connected by light, flexible spokes of 8.9 m and 5.3 m length that can be elongated or shortened. What is the new angular speed if each of the spokes to shortened by 84% of their original length? An effect similar to this occurred in the early stages of the formation of our galaxy. As the massive cloud of gas and dust contracted, an initially small rotation increased with time. Answer in units of rev/s

Explanation / Answer

the initial angular momentum is I1w1 = 2*(m1*r1^2+m2*r2^2)*w1 here m1=5.3 = m2 r1 = 5.3 and r2 = 8.9 m w1 = 5 rev/s now the the final angular momentum is I2*w2 = 2*(m1*r1^2+m2*r2^2)*w2*(0.84^2) since the angular momentum remains constant we have I1*w1 = I2*w2 => w2 = w1/(0.84^2) = 7.086 rev/s

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