Question

What are the two main conditions for equilibrium?

Answer 1

In physics, equilibrium is the state of a system where neither its state of motion nor its internal energy state changes over time. When a body is either in uniform motion (both translational and rotational) or at rest, it is said to be in equilibrium. We say a body is in static equilibrium in an inertial frame of reference when it neither rotates nor moves in translational motion in that frame of reference.

Complete step by step answer:
The following are the two main conditions for equilibrium:
I condition:
The first requirement is that the object's net force be zero. If the net force is zero, there is no net force in any direction.
Let's say $n$ forces are acting on a body:
$F1,{\text{ }}F2,{\text{ }}F3,{\text{ }}......,{\text{ }}Fn$.
${F_1}\; + {F_2} + {F_3} + \ldots \ldots + {F_n}\; = 0$ or $\sum F{\text{ }} = 0$ …… $\left( 1 \right)$
The symbol $\sum$ is a Greek letter called sigma used for summation. The equation $\left( 1 \right)$ is called the first condition of equilibrium.
The first requirement for equilibrium can be expressed as follows in terms of the X and Y components of the forces operating on the body:
${F_{1x}}\; + {F_{2x}} + {F_{3x}} + \ldots \ldots + {F_{nx}}\; = 0$
And,
$F1y + F2y + F3y + \ldots \ldots + {F_{ny}} = 0$
(or)
$\sum Fx = 0$
$\sum Fy = 0$
II condition:
The second criteria are that a rotating item is in equilibrium if its rate of rotation is constant and unaffected by external influences. $\sum \;\tau = 0$

Note:
Examples for the first condition of equilibrium:
On a table, there is a book.
The first criterion for equilibrium is satisfied by a picture hanging on a wall, which is at rest.
A paratrooper falling at terminal velocity also meets the first criteria for equilibrium, indicating that he/she is in equilibrium.
Examples of second condition equilibrium:
The force exerted on the car's steering,
Couple,
The children who were playing in the sea saw.