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I was doing some questions in rotational mechanics and I am not able to understand the concept behind hinge reaction which acts on a rod suspended at a point. I am taking a simple example here. Let's say that a uniform rod of some mass is free to rotate. Initially it's at rest in an unstable equilibrium vertically upwards. The hinge reaction acting initially would be -mg upwards. If the rod is slightly displaced and then makes some angle, hinge reaction will change but will not be 0.

My query is-

1 .Will the work done by hinge reaction be 0 somehow?

2 .Will the total mechanical Energy of the rod be conserved?

3 .If the total mechanical Energy is not conserved then how can we calculate the angular velocity of rod after it makes some angle theta?

I have done some similar questions in past and as far as I remember, I used conservation of energy. I was not familiar with hinge reaction at that time.

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  • $\begingroup$ Well, does the hinge force ever have a component along the displacement of the rod? $\endgroup$ – BioPhysicist Nov 17 '18 at 16:42
  • $\begingroup$ I thought about it and I am not sure but I think it does have component in the direction of motion of center of rod at that particular instant. $\endgroup$ – Vedansh Agrawal Nov 17 '18 at 17:00
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    $\begingroup$ The hinge force is directed along the rod, and the motion of center of the rod is perpendicular to the rod. $\endgroup$ – BioPhysicist Nov 17 '18 at 17:01
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    $\begingroup$ Possibly related to Carroll's paradox? $\endgroup$ – Chemomechanics Nov 17 '18 at 19:50
  • $\begingroup$ @Chemomechanics Yes. Got it. The hinge reaction has no component in direction of motion. $\endgroup$ – Vedansh Agrawal Nov 18 '18 at 2:22

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