It is expensive to carry things in space In the problem bell

It is expensive to carry things in space. In the problem bellow you will learn about a system that has small mass and can effectively de-spin satellites. To solve the problem you may want to apply conservation of angular momentum. You may use your calculator. Problem: De-spinning of satellites: Satellites are often designed to rotate to maintain their stability. Sometimes it is necessary to de-spin them-that is, to reduce their angular speed. Two small objects, called yo-yos, each of mass m=l. 0 kg, are attached to the satellite by cords of length 1=61m, which are wrapped around the satellite in a plane perpendicular to its angular velocity. To de-spin, the latches holding the yo-yos are opened and cords unwind. The cords are designed to separate from satellite when they make an angle phi=80degree with the satellite surface. If the initial spin rate is omega _i =6.0 rad/s, the satellite\'s rotational inertia is 1=150 kgm^2, and its radius is 1.0m, what is the satellite\'s final spin rate

Solution

Initial Angular Momentum = IWi
Final Angular Momentume = IWf + 2mr^2 * Wf
Now, r = sqroot(l^2 + R^2 + 2Rlcos(theta)) = sqroot(61*61 + 1 +12*cos(80)) = 61.025m
Final Angular Momentum = ( I + 2*1*61.025^2 )Wf = IWi
Wf = 150 * 6 / [150 + 7448.167] = 0.11844 rad /s