A 93.5-kg horizontal circular platform rotates freely with no friction about its

Question

A 93.5-kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.51 rad/s. A monkey drops a 9.03-kg bunch of bananas vertically onto the platform. They hit the platform at 4/5 of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 21.9 kg, drops vertically to the edge of the platform, grasps it, and continues to rotate with the platform. Find the angular velocity of the platform with its load. Model the platform as a disk of radius 1.79 m.

Explanation / Answer

conservation of angular momentum

initial angular momentum = final angular momentum

I1 W1 = I2W2

here I1 is momento fo inertia of disc rotating about its centre is mr^2/2

and treating the bananas and mass as point objects then their momento f inertia is mr^2

now

                            mr^2 / 2*W1 = (Ib + Im) W2

W2 = (mr^2 / 2*W1 )/(Ib + Im)       Ib= mb*r^2, Im = Mm*r^2

given radius of the disc is 1.85 m     ==> Ib= 8.77((4/5)*1.85)^2 = 19.20 kg m^2

                                                                        Im = 21.2(1.85)^2    = 72.557 kg m^2

W2 = ((91.3*(1.85)^2)/2)(1.79) ) / (19.2+72.557) = 3.0478 rad/s

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