Newton's Laws

When it comes to body dynamics, the image that comes to mind is Isaac Newton's classic and mythological image, reading his book under an apple tree. Suddenly an apple falls on your head. It is reported that this was the first step in understanding gravity, which attracts the apple.

With the understanding of gravity came the understanding of Force, and Newton's three Laws.

In kinematics, one studies motion without understanding its cause. In dynamics, we study the relationship between force and motion.

Force: It is an interaction between two bodies.

The concept of force is intuitive, but to understand it, it can be based on effects caused by it, such as:

Acceleration: Causes the body to change its speed when a force is applied.

Deformation: Causes the body to change its shape when it is under the action of a force.

Resulting Force: It is the force that produces the same effect as all the others applied to a body.

Given various forces applied to any body:

The resulting force will be equal to the vector sum of all applied forces:

Newton's laws constitute the three fundamental pillars of what we call Classical Mechanics, which is precisely why it is also known as Newtonian Mechanics.

Newton's First Law - Principle of Inertia

  • When we are in a car, and the car goes around a curve, our body tends to remain at the same vector velocity as it was before the curve, it gives the impression that it is being "thrown" to the opposite side of the curve. This is because the vector velocity is tangent to the trajectory.
  • When we are in a moving car and it suddenly brakes, we feel as if we are thrown forward, as our bodies tend to keep moving.

These and several other similar effects are explained by the principle of inertia, the wording of which is:

"A body at rest tends to remain at rest, and a body in motion tends to remain in motion."

So it follows that a body changes its state of inertia only if someone or something applies a resulting force other than zero to it.

Newton's 2nd Law - Fundamental Principle of Dynamics

When we apply the same force to two bodies of different masses, we see that they do not produce equal acceleration.

Newton's 2nd law says that Force is always directly proportional to the product of a body's acceleration by its mass, namely:

or in module: F = ma


F is the resultant of all forces acting on the body (at N);

m is the body mass at which forces act (in kg);

a is the acquired acceleration (in m / s²).

The unit of force in the international system is N (Newton), which is equivalent to kg m / s² (kilogram meter per second squared).


When a force of 12N is applied to a 2kg body, what is the acceleration gained by it?

F = ma

12 = 2a

a = 6m / s²

Tractive force

Given a system where a body is pulled by an ideal wire, ie it is inextensible, flexible and has negligible mass.

We can consider that the force is applied to the wire, which in turn applies a force to the body, which we call tensile force. .

Newton's 3rd Law - Principle of Action and Reaction

When a person pushes a box with an F force, we can say that it is an action force. but according to Newton's third law, whenever this occurs, there is another force with equal modulus and direction, and opposite to the force of action, this is called the reaction force.

This is the principle of action and reaction, whose statement is:

"Forces always act in pairs, for every action force there is a reaction force."