Components Form of Newton’s Second Law

In a two-dimensional problem, we must use a free-body diagram. To construct a free-body diagram, first, the forces must be resolved into x and y components. Then, we can apply the second law in each direction: Forces acting in the x direction are responsible for the acceleration along the x direction, and forces acting in the y direction are responsible for acceleration along the y direction. This allows us to calculate, correspondingly, the x component and y component of the acceleration vector of our system.

Figure 1: Newton's second law of motion expressed in components for each direction. The sum of the projection of all forces along the x-axis equals the mass times the acceleration along the x-axis. The sum of the projection of all forces along the y-axis equals the mass times the acceleration along the y-axis.