Question

Please solve this question, and show steps. Thank you so much.

A 90.9 kg horizontal circular platform rotates freely with no friction about its center at an initial angular velocity of 1.73 rad/s. A monkey drops a 8.01 kg bunch of bananas vertically onto the platform. They hit the platform at of its radius from the center, adhere to it there, and continue to rotate with it. Then the monkey, with a mass of 20.5 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 1.73 m. angular velocity: rad/s rad/s

Answer 1

This is the question of conservation of angular momentum. Since no external force is acting on the system hence angular momentum remains conserved. :: Initial angular momentum = final angular momentum. angular mementum = I w Initially Is= moment of inertical of disc - MR? - 90.9 x 1.73? 2 Id = 136 kg m². Initial angular = 136 x 1.73 = 235.33 mom entum

Finally of of Ip = disc with moment banana inertia & monkey = MR² + Mm R² + Mg x H R ) 2. where Mm = mass of monkey My= mass of bananas = 136 + 61.35 + 15.34 If = 212.69 kg m² Let final angular velocity = w f. .: 235.33 = If wf = 212.69x Wf .: wf = 1.106 rad/s :