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.