Newton's Second Law


Newton's second law establishes the result of applying a net external force to an object.


Newton's Second Law is:   .

This equations states that the necessary net force to accelerate an object is proportional to the mass of the object. In addition, this equation is the foundation for defining the unit of force, the Newton .

The previous equation is between the net external force acting on the object and the mass and acceleration of the object. As indicated above, a net force is the vector addition of forces, . External force means that the corresponding force is applied by a different object over the object of mass m that accelerates as a consequence of the applied force.


In order to understand the meaning of external force, think (or try out) the following situation: Can the man on the left lift himself to the top of the table by pulling in his shoelaces? The answer to this question is clearly no. Why? No matter how strong the man is, he will not be able to lift himself to the top. The force that he is exerting in himself is not an external force. Notice that the force that he applies with either of his hands on the shoelaces is compensated by an equivalent force, on the hand, pulling the man down, see action and reaction. Therefore, the net effect on the man is zero force.

Since the shoes are secure to the man, the shoes are part of the man. Thus a force exerted on the shoes is a force exerted on the man. When the man exerts a force on the shoes, he is exerting a force in himself.



Newton's second law is a relation between vectors. Since masses are always positive, the direction of the net external force and the direction of the acceleration of the object are the same. Thus, the single vectorial form of Newton's second law can be represented by three equations, one per each component.

The vector nature of the last summation is maintained because it has not been specified if those component points toward the positive or negative direction of the corresponding axis (see below).

In this notes, only two dimensional vectors will be studied (plane of the board or plane of the screen). Therefore, the z-component of the vectors is assumed to be null. 

For the x-component of the vectors, the convention used in this notes is that vectors pointing to the right are positives while vectors pointing to the left are negatives. At the same time, for the y-component of the vectors, the convention is that vectors pointing up are positive and vectors pointing down are negative.


If is positive, the resultant vector is pointing to the right. if negative, the resultant vector points to the left.

If is positive, the resultant vector is pointing up. if negative, the resultant vector points down.




Newton's second law, , is a relation between mass, acceleration, and force. The force is proportional to the acceleration with the proportionality constant being the mass. Thus, if an object is accelerating, a net external force must be acting on the object and vice versa.

The definition of weight is a direct result of Newton's second law. Accordingly with Galileo Galilei, all objects fall with the same acceleration, the acceleration of gravity g. Considering Newton's second law, to this acceleration there is a force associated with it, this force is called the weight.

Weight :


Direction: Always pointing toward the center of the Earth. This means that near the surface of the Earth, the direction of the weight is always a vertical vector pointing down.



by Luis F. Sez, Ph. D.    Comments and Suggestions: LSaez@dallaswinwin.com