Conditions of Equilibrium

There are two conditions of equilibrium.

First Condition of Equilibrium

"An object is said to be in equilibrium if the sum of all the forces acting on it in one direction balances the sum of all the forces acting in the opposite direction”. 

        It means that if the net force of all acting forces or the resultant force is zero then the object will be in static equilibrium.

        If the forces are acting in two dimensions i.e. x-component and y-component, then the first condition of equilibrium can be given as:

                                                  
                                                  

Examples: 

            If two forces and are equal in magnitude and they are acting on a ring in opposite direction then the ring will remain at rest.

Second Condition of Equilibrium

“For an object to be in equilibrium the net turning effect of forces acting on the object must be zero i.e. the sum of the clockwise torques must be equal to the sum of the anticlockwise torques”

Mathematically it can be expressed as,

                                                            
Example:

              A meter rod with a hole at its centre is suspended by means of a nail on a wall. We then apply two equal but opposite forces at point X and Y. As the upward force at Y is equal to the downward force at X, the body executes rotational motion.

Centre of Gravity:            

                 The centre of gravity of a body is defined as a point at which the whole weight of the body appears to act. This point may be inside or outside the body.

Three States of Equilibrium:

                   There are three states of equilibrium.

1-Stable Equilibrium:

            A body on being displaced if it has tendency to come back to its initial position then it is said to be in Stable Equilibrium.

OR

            It can also be defined as if the point of support is above the centre of gravity then it is said to be in Stable Equilibrium.

Example:

           If a book is lifted from its edges and then allowed to fall it will come back to its original position. Chair, table and other bodies lying on the floor are the examples of stable equilibrium.

2-Unstable Equilibrium:

           When a body on being displaced topples over and takes a new position then it is said to be in state of Unstable Equilibrium.

OR

               It can also be defined as if the point of support is below the centre of gravity then the body is said to be in Unstable Equilibrium.

Example:

          If a pencil standing vertically is slightly disturbed from its position, it will not come back to its original position.

3-Neutral Equilibrium:

           When a body on being displaced neither it topples over nor it takes its original position then the body is said to be in Neutral Equilibrium.

OR

        It can also be defined as if the point of support is on the centre of gravity then the body is said to be in Neutral Equilibrium.

 Example:

         If a ball is pushed slightly to roll, it will neither come back to its original position nor it will roll forward rather, it will remain at rest.