What do you mean by the term "equilibrium"? What are equilibrium of rest and equilibrium of motion? State the conditions for complete equilibrium of a body.
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Equilibrium: A body or a system of particles is said to be in a state of equilibrium if inspite of a number of forces or torques acting on it, the body or the system of particles remains in its original state of rest or of uniform motion (translational or rotational or both). Thus, equilibrium state means that acceleration (both linear as well as angular) of the body/system must be zero. Hence, equilibrium is of two types:
For equilibrium $\vec{\text{p}}=\text{a constant or }\frac{\text{d}\vec{\text{p}}}{\text{dt}}=0$
$\text{ or }\sum\vec{\text{F}}_{\text{ext}}=0$
Hence for rotational equilibrium, the vector sum of all the external torques acting on the system/ body must be zero.
For equilibrium $\vec{\text{L}}=\text{a constant or }\frac{\text{d}\vec{\text{p}}}{\text{dt}}=0$
$\text{ or }\sum\vec{\tau}_{\text{ext}}=0$
- Equilibrium of rest: If a given system remains in a state of rest and does not change its position inspite of number of forces acting on it, it is said to be in an equilibrium of rest e.g., our house, our school etc.
- Equilibrium of motion: If a given system maintains its state of uniform motion, translational or rotational or combined, under the action of a number of forces then it is said to be in an "equilibrium of motion" e.g., our Earth, the planetary system, electrons revolving around the nucleus of an atom. For a state of equilibrium of motion, the value of linear momentum and/ or angular momentum of the system should have a finite and constant value.
- For translational motion,
For equilibrium $\vec{\text{p}}=\text{a constant or }\frac{\text{d}\vec{\text{p}}}{\text{dt}}=0$
$\text{ or }\sum\vec{\text{F}}_{\text{ext}}=0$
Hence for rotational equilibrium, the vector sum of all the external torques acting on the system/ body must be zero.
- For rotational motion,
For equilibrium $\vec{\text{L}}=\text{a constant or }\frac{\text{d}\vec{\text{p}}}{\text{dt}}=0$
$\text{ or }\sum\vec{\tau}_{\text{ext}}=0$
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