What force is the pin exerting on the rod?

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SUMMARY

The discussion focuses on the forces exerted by a pin on a rod attached to a ceiling and a wall. At time t = 0 seconds, the force of the pin is calculated to be mg/4, while the tension in the rope is mg/2. As the rod swings vertically, the relationship between angular speed and angular acceleration is explored, emphasizing the need for a free-body diagram and the conservation of energy to analyze the system. The discussion concludes with the need to determine the force of the pin when the rod reaches a horizontal position.

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A thin rod of uniform mass M and length L is attached to a string at one end to the ceiling and a pin at the other end to the wall. The rope (connecting the ceiling and the horizontal rod) is cut at t = 0 s.

1) What is the force of the pin at t = 0 seconds?

2) When the rod swings vertically, what force is the pin exerting on the rod?

3) When the rod reaches the vertical part of its swing, what is the rod's angular speed and angular acceleration?

4) If the initial position of the rod was almost vertical, what would be the force of the pin when it has reached horizontal position.



L/2 mg sin90 = I [tex]\alpha[/tex]



I got force of pin for the initial condition = mg/4 and tension of rope = mg/2. A t=0 accerlation of center of mass I got -3/4g. All the above questions I have no idea how to set up.
 
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Start with a free-body diagram. You will find that you need a relationship between the angular speed of the rod and how much it rotated by. No problem: use the conservation of energy.
 

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