Equilibrium of Forces In Physics


Forces that have zero resultant and zero turning effect will not cause any change in the motion of the object to which they are applied. such forces are said to be in equilibrium. for understanding the equilibrium of an object under two or more concurrent coplanar forces latest first discuss the resolution of forces and moment of a force about some point.

Resolution of forces-

when a force is applied by an equivalent set of components, it said to be resolved. one of the most useful ways in which to resolve a force is to use only two-component. which are at the right angle also the magnitude of these components can very easily found using trigonometry.

Suppose a force f acting with angle theta from the horizontal then its horizontal and vertical component is equal to-

\(\begin{aligned}F_{x}=F\cos \left( \theta \right) \\and\\ F_{y}=F\sin \left( \theta \right) \end{aligned}\)

Finding such components is referred to as resolving a force in a pair of perpendicular directions. not that the component of a force in a direction perpendicular to itself is zero. similarly, the component of a force in a direction perpendicular to the force is equal to the magnitude of the force.

For example component of the force in the direction of Forces will be F.


Moment of force and sometimes it’s called torque. the magnitude of torque also known as the moment of force F is calculated by multiplying together the magnitude of the force F and its perpendicular distance from the axis of rotation.


The direction of the torque is always perpendicular to the plane of force and radial vector. it is also calculated by screw rule. We generally take anticlockwise torque positive that is outward of the plane and clockwise torque negative that is inward to the plane.

Coplanar forces in equilibrium-

When an object is in equilibrium under the action of a set of two or more coplanar forces, each of three factors which comprises the possible movement of the object must be zero that is the object has-

  • No linear movement along with any two mutually perpendicular directions.
  • No rotation about any axis.
  • The set of forces must, therefore, be such that
    The algebraic sum of the component parallel to the X-axis is zero.
  • The algebraic sum of the component parallel to the y-axis is zero.
  • The resultant moment about any specific axis is also zero.
     Condition for a body is in equilibrium-
    Net forces along the individual axis are equal to zero and talk about any axis is equal to zero.

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