The system of small objects shown in the figure is rotating about an axis throug

Question

The system of small objects shown in the figure is rotating about an axis through the center and perpendicular to the paper at an angular speed of 2.00 rev/s. The objects are connected by light, flexible spokes that can be lengthened or shortened. What is the new angular speed if the spokes are shortened 0.50 m? What would be the new angular speed if one of the rods was replaced while rotating with a rod of the same length, but with a mass m?

The system of small objects shown in the figure is rotating about an axis through the center and perpendicular to the paper at an angular speed of 2.00 rev/s. The objects are connected by light, flexible spokes that can be lengthened or shortened. What is the new angular speed if the spokes are shortened 0.50 m? What would be the new angular speed if one of the rods was replaced while rotating with a rod of the same length, but with a mass m?

Explanation / Answer

applying conservation of angular momentum we have

4*m*1^2*2=4*m*0.5^2*w2

w2=8 rev/s ans

For second case center of mass of rod is 0.5 m from the revolution so we have

4*m*1^2*2=(3m*1^2+m*0.5^2)*w2

w2=4.92 rev /s ans

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