According to Newton's first law, we know that a body is at rest or in straight and uniform motion if the resultant of the forces acting on it is nil. In this case we say that the body is in balance, which in turn can be static, when the body is at rest; or dynamic, when the body is in motion.
Point P, in the figure below, is subject to the action of three forces 
. This point is at rest.
Therefore, we can say that this point is in static equilibrium, as it satisfies the equation:
It is important to say that the vector sum of each of the forces must be made, and transform this vector equation into a scalar equation.
If the forces acting on the material point are coplanar, the vector equation of the sum of the forces in two scalar equations, projecting the forces onto orthogonal X and Y Cartesian axes. Therefore, the equilibrium conditions of the material point can be established as follows:
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The projection will be positive if its direction coincides with the axis direction, and it will be negative if its direction is opposite to the axis direction. The projection will be equal to zero when the force has a direction perpendicular to the axis.
In the figure we can see that the forces F2 and F3 are in the direction of the Y and X axes, respectively, and the force F1 forms an angle Ө with the X axis.
In this case, the components of force F1 in the direction of the X and Y axes are, respectively:
F1x = F1.cosӨ
F1y = F1.sinӨ
See how the projection of all forces in the Cartesian coordinate system looks like:
By Kleber Cavalcante
Graduated in Physics
Brazil School Team
mechanics - Physics - Brazil School
Would you like to reference this text in a school or academic work? Look:
CAVALCANTE, Kleber G. "Balance of a Material Point"; Brazil School. Available in: https://brasilescola.uol.com.br/fisica/equilibrio-um-ponto-material.htm. Accessed on June 27, 2021.
