Newton's Second Law is often stated as the vector equation F = m*a, where F is the net force on an object and a is the object's acceleration.  Thus, in two dimensions the law can be stated in scalar form as: where F_x and F_y are the components of the net force along the x and y axes, and a_x and a_y are the components of the object's acceleration along the x and y axes.

Notice that F stands for the net force on the body and not for an individual force.  The distinction between the net force and an individual force is that each individual force is due to the interaction between the body and some other object, whereas the net force is the sum of all such forces and is thus not due to any particular object.

Most solutions immediately reduce F_x or F_y to the appropriate sum of individual forces.  Thus, the most frequently used form of Newton's Law is:

where F1, F2, F3, etc. are the individual forces acting on the body.  For instance, if the body is acted on by a weight force named W and a tension force named T, then we have Note that this only holds if W and T are the only forces acting on the body.  The sum of forces must include all the forces acting on the body.

When the object's acceleration is zero, then the equations simplify to

This is sometimes called Newton's first law, but it is just a special case of Newton's second law.  It holds only when the velocity of the body is constant, which means that the acceleration of the body is zero.

A good way to determine all of the forces acting on a body is to attribute at least one force to each thing touching the body and then add additional forces for things that can exert a force without touching.  The first class of forces is called contact forces and include, tension force due to a rope or string), normal force due to a surface, friction force due to a surface, applied force due to someone pushing or pulling, drag force due to a fluid, etc.  The second class of forces are called action at a distance forces and include weight force due to gravity, electrical forces due to charge and magnetic forces due to moving charges.