The body of the satellite shown has a weight that is negligible with respect to

Question

The body of the satellite shown has a weight that is negligible with respect to the two spheres A and B that are rigidly attached to it, which weigh 149 lb each. The distance between A and B from the spin axis of the satellite is R = 3.6 ft. Inside the satellite there are two spheres C and D weighing 5.8 lb mounted on a motor that allows them to spin about the axis of the cylinder at a distance r = 0.71 ft from the spin axis. Suppose that the satellite is released from rest and that the internal motor is made to spin up the internal masses at a constant time rate of 5.0 rad/s2 for a total of 10 s. Treating the system as isolated, determine the angular speed of the satellite at the end of spin-up. As the system is released from rest and there are no external moments acting on the system, the total angular momentum of the system must remain equal to zero. The angular momentum of the satellite must offset the angular momentum of the two internal spheres as they spin up.

Explanation / Answer

Hey :) So, there's nothing too tricky to this problem, besides knowing where to start! The big thing for this is knowing that I (rotational moment of inertia) = mass*radius^2 And you also have to know that L (angular momentum) = I * w (angular velocity) 5.0 rad/s^2 is angular acceleration, and after ten seconds the angular velocity would be equal to 50 rad/s. Putting those two together you get this: L(inside spinning weights) = L (outside spinning weights) m(inside)L^2*w=m(outside)L^2*w 2*5.8lbs*0.71feet^2*50rad/s=2*149lbs*3.6feet^2*w

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