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Physics of Using Dumbbells and Case of George of the Jungle

A student sits on a freely rotational stool holding two dumbbells, each of mass 3.00 kg. When the students arms are extended horizontally as in figure, the dumbbells are 1.00 m from the axis of rotation and the student rotates with an angular speed of 0.750 rad/s. The moment of inertia of the student plus stool is 3.00 kg and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.300 m from the rotation axis. (a) Find the new angular speed of the student. (b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward.

My Weight is 149.69 kg (330 lbs)
Weights that I held = 3.63 kg (8 lbs)
Time it took to make 1 full rotation with the weights held out as in figure (a) = 2.19 sec
Time it took to make 1 full rotation with my arms held in as if figure (b)

George of the jungle, with mass m, swings on a light vine hanging from a stationary tree branch. A second vine of equal length hangs from the same point, and a gorilla of larger mass M swings in the opposite direction on it. Both vines are horizontal when the primates start from rest at the same moment. George and the Gorilla meet at the lowest point of their swings. Each is afraid that one vine will break, so they grab each other and hang on. They swing upward together, reaching a point where the vines make an angle of 35.0 with the vertical. (a) Find the value of the ratio n/M. (b) What if? Try the following experiment at home. Tie a small magnet and a steel screw to opposite ends of a string. Hold the center of the string fixed to represent the tree branch, and reproduce a model of a motions of George and the Gorilla. What changes in your analysis will make it apply to this situation? What if? Next assume the magnet is strong so that it noticeably attracts the screw over a distance of a few centimeters. Then the screw will be moving faster immediately before it sticks to the magnet. Does this extra magnet strength make a difference?

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This solution provides a detailed, step by step explanation of the given physics problem.