Physics
Equilibrium of Bodies
Bodies in Equilibrium
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⚡ Quick Summary
A body is in equilibrium when the net external force and net external torque acting on it are zero. Equilibrium can be stable, unstable, or neutral depending on how the body responds to small displacements.
F = Ma, G = Ia
- Translational Equilibrium: The centre of mass of a body remains in equilibrium if the total external force acting on the body is zero. (F = Ma)
- Rotational Equilibrium: A body remains in rotational equilibrium if the total external torque acting on the body is zero. (G = Ia)
- For a body at rest in an inertial frame, the total external force should be zero in any direction, and the total external torque should be zero about any line.
- When forces lie in a single plane (X-Y plane):
- ΣFx = 0
- ΣFy = 0
- ΣGz = 0 (Torque about any line perpendicular to the plane is zero)
- Equilibrium Types:
- Stable Equilibrium: Body tries to regain its equilibrium position after slight displacement. The center of mass goes higher when slightly displaced.
- Unstable Equilibrium: Body gets further displaced after slight displacement. The center of mass goes lower when slightly displaced.
- Neutral Equilibrium: Body stays in equilibrium even after slight displacement. The center of mass stays at the same height.
- For a body placed on a horizontal surface, the torque of the contact forces about the center of mass should be zero to maintain equilibrium. This happens only if the vertical line through the center of mass cuts the base surface at a point within the contact area.