What is Newton’s Second Law?

We explain to you what Newton’s Second Law is, what its formula is and in what experiments or examples of everyday life can be observed.

  1. What is Newton’s Second Law?

Newton’s Second Law or Fundamental Principle of Dynamics is the second of the theoretical postulates made by British scientist Sir Isaac Newton (1642-1727) based on previous studies by Galileo Galilei and René Descartes.

Just like his Law of Inertia , it was published in 1684 in his work Mathematical Principles of Natural Philosophy , one of the fundamental works of the modern study of physics . This law expresses, in the words of the scientist in Latin:

“ Mutationem motus proportionalem esse vi motrici impressæ, & fieri secundum lineam rectom qua vis illa imprimitur ”


” The change of movement is directly proportional to the printed driving force and occurs along the straight line along which that force is printed .”

This means that the acceleration that a given body experiences is proportional to the force that is printed on it, which may or may not be constant. The essence of what is proposed by this second law has to do with the understanding that force is the cause of the change of movement and speed .

  1. Newton’s Second Law Formula

Newton's Second Law Acceleration Force Speed ​​Mass Formula
By the formula of Newton’s Second Law, force, mass or acceleration can be calculated.

The fundamental formula of this Newtonian principle is:

F = ma

F is the force.

m is the body mass.

A is the acceleration.

Hence, the acceleration of an object can be calculated by applying the formula a = ƩF / m , with the proviso that ƩF is the net force applied to the body. This means that if the force exerted on an object doubles, so will its acceleration ; while if the object’s mass doubles, its acceleration will become half.

  1. Experiments on Newton’s Second Law

A simple experiment to perform and which proves Newton’s second Law involves nothing more than a bat and several balls. The latter must be supported and motionless on a podium, and will be hit with the bat with the same amount of force.

The balls will be classified by approximate weight, to notice how the same force exerted results in a greater or lesser acceleration depending on the mass of each ball.

Another possible experiment involves the same balls of different mass, which on this occasion will be dropped in a straight line (free fall) so that only gravity acts on them . Since the latter is a constant force, the difference in mass is the only criterion for some to achieve greater acceleration, and therefore they will first touch the ground.

  1. Examples of Newton’s Second Law

Newton's Second Law Acceleration Force Speed ​​Mass Example
To move objects of greater mass, a greater force is required.

A simple example of the application of this Newton’s Second Law occurs when we push a heavy object . Being the object in stillness, that is, with acceleration equal to zero, we can set the object in motion by exerting on it a force that overcomes inertia and that gives it a certain acceleration.

If the object is extremely heavy or massive, that is, it has a large mass, we must exert greater force to increase its movement.

Another possible example is a car that speeds up, thanks to the force that the engine prints on it . The greater the force exerted by the work of the engine, the greater the speed the car will reach, that is, the greater the acceleration. A more massive car, for example a truck, will need more force to achieve the same acceleration than a lighter one.

  1. Newton’s other laws

Apart from Newton’s Second Law, the scientist proposed two other fundamental principles, which are:

  • The Law of inertia , which reads: “Every body perseveres in its state of rest or uniform rectilinear motion unless it is forced to change its state by forces printed on it.” This means that an object moving or at rest will not alter its state unless some kind of force is applied.
  • The Law of action and reaction , which reads: “Every action corresponds to an equal reaction but in the opposite direction: it means that the mutual actions of two bodies are always the same and directed in the opposite direction.” Which means that for each force exerted on an object, a similar one exerted by it is opposed, in the opposite direction and of equal intensity.

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