Force on a Swinging Rod (space elevator)

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SUMMARY

The discussion focuses on the physics of a swinging rod scenario related to the space elevator problem. It establishes that the force exerted by the hand on a vertical rod is given by the formula F = m[g - w²(ra + l/2)], where m is the mass, g is the gravitational acceleration, w is the angular speed, ra is the arm length, and l is the length of the rod. Additionally, participants explore how to derive an expression for the rod length l that results in zero force exerted by the hand. The conversation emphasizes the importance of considering both torque and gravitational forces in solving the problem.

PREREQUISITES
  • Understanding of angular motion and forces
  • Familiarity with torque calculations
  • Knowledge of gravitational force concepts
  • Basic principles of rotational dynamics
NEXT STEPS
  • Study the derivation of torque in rotational systems
  • Learn about the effects of angular velocity on forces in circular motion
  • Explore gravitational force equations in dynamic systems
  • Investigate the principles of equilibrium in rotating bodies
USEFUL FOR

This discussion is beneficial for physics students, educators, and engineers interested in dynamics, particularly those exploring concepts related to rotational motion and gravitational effects in mechanical systems.

msion
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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!
 
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