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This is part of the space elevator problem. It starts with a swinging rod scenario:
1. Suppose that you swung a rod of mass m and length l at angular speed w in a vertical circle with your shoulder as the axis. The distance ra is the length of your arm, which is the distance from the bottom of the rod to the axis of rotation. Take up as the positive z direction, and show that the force that must be exerted by the hand on the rod when the rod is vertical above the hand is:
F=m [g-w2(ra+l/2)]
2. Find an expression for l that will result in zero force exerted by your hand.
I am completely lost, how to start this problem? I am thinking of applying torque, Ia = rF, and find the force that way, but this will exclude the gravitational force. Any ideas? Thanks a lot!
1. Suppose that you swung a rod of mass m and length l at angular speed w in a vertical circle with your shoulder as the axis. The distance ra is the length of your arm, which is the distance from the bottom of the rod to the axis of rotation. Take up as the positive z direction, and show that the force that must be exerted by the hand on the rod when the rod is vertical above the hand is:
F=m [g-w2(ra+l/2)]
2. Find an expression for l that will result in zero force exerted by your hand.
I am completely lost, how to start this problem? I am thinking of applying torque, Ia = rF, and find the force that way, but this will exclude the gravitational force. Any ideas? Thanks a lot!
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