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The first condition of equilibrium is when a body at rest or moving with uniform velocity has zero acceleration. From Newton's Law of Motion the vector sum of all forces acting on it must be zero. This is known as the first condition of equilibrium. Using the mathematical symbol ∑F for the sum of all forces we can write.
∑F = 0
In the case of coplanar forces, this condition is expressed usually in terms of x and y components. It may be noted that if the rightward forces are taken as positive then leftward forces are taken as negative.

For angular acceleration to be zero, the net torque acting on the body should be zero. Thus for a body in equilibrium, the vector sum of all the torques acting on it about any arbitrary axis should be zero. This is known as second condition of equilibrium. Mathematically it is written as:
∑T=0
By convention, the counter clockwise torques are taken as positive and clockwise torques as negative.
When 1st condition is satisfied, there is no linear acceleration and body will be in translational equilibrium. When 2nd condition is satisfied, there is no angular acceleration and body will be in rotational equilibrium.

The Second Condition of Equilibrium was presented by Issac Newton. According to this condition, an object that is in equilibrium does not move along a straight line. Which means that the the sum of all forces applied on it is zero.

Also, the sum of all the rotational forces on the object is zero due to which the object does not rotate. Thus, the second condition of equilibrium states that the sum of all the torques on an object that is in equilibrium are zero.