Newton's Second Law, Fundamental Law of Dynamics

Newton's second law, fundamental law of dynamics

Newton's second law is one of the three laws of motion developed by the physicist and mathematician Sir Isaac Newton (1642-1727). This law, together with the law of inertia and the law of the principle of action and reaction published in his masterpiece "Philosophiae naturalis principia mathematica" (Mathematical principles of natural philosophy).

Newton wrote the second law in his Principia Mathematica as follows:

“The change in movement is proportional to the force imposed; and it is made in the direction of the straight line in which the force is imposed. "

Explained in a more colloquial way, Newton's second law indicates that if we apply a force on an object, the object will experience an acceleration directly proportional to the force. That is, the action of pushing an object with a force F implies that the state of rest or motion of the object varies.

Newton's Second Law Formula

This can be written analytically as:

F = m a


  • F is the sum of the net forces acting on the object expressed in newtons.

  • m is the mass expressed in kilograms.

  • a is the acceleration expressed in meters per second squared.

The mass of an element has a proportionality function between the resultant force exerted on the element and its acceleration. This implies that, by exerting the same force on two objects with different masses, the acceleration of the object will be greater in the one with less mass. In reality, the mass of an element generates a resistance to the variation of its speed. For this reason, mass is sometimes called inertial mass (resistance to change).

In a moving object, if the direction of force is the same as that of velocity, the object will accelerate. If, on the other hand, the force exerted is in the opposite direction, the object will slow down.

A particular case of this formula is when it is applied to the force of gravity on the surface of the Earth. Any object in free fall on the earth's surface experiences an acceleration of 9.8 m / s² regardless of its mass. This value is obtained from Newton's own law of universal gravitation.

What Is the Definition of Force?

A force is the element that causes an object to accelerate.

The resultant of all the forces exerted on an object has the same direction and sense as the acceleration (which can be different from the speed). The modulus of the resulting forces is directly proportional to the modulus of acceleration as stated in Newton's second law formula.

What Is the Unit of Force?

The newton is the unit of force in the international system of units that is given by the fundamental principle of dynamics (Newton's 2nd law) as:

1 N = 1 kg m / s²

If an object of mass one kilogram has an acceleration of one meter per second squared with respect to an inertial reference frame, then the resultant force exerted on the object is one newton.


Published: November 10, 2021
Last review: November 10, 2021