# Equation of Newton's Three Laws

## F = ma

Automatic translation Updated March 26, 2023

Newton's famous laws (1642-1727) are fundamental in classical mechanics, they describe the movement of an object under the action of forces. Newton's first two laws are described in Latin in the original edition of the Principia Mathematica of 1687.

Newton's three laws:
• Newton's first law, also known as the principle of inertia, states that every body perseveres in its state of rest or uniform motion in a straight line, unless some force acts on it. This means that if no force is exerted on the object it is either stationary or in uniform rectilinear motion. Moreover, it was Galileo (1564-1642) who first described this phenomenon.
• Newton's second law states that the force applied to a body is proportional to the acceleration it produces.
This law can be expressed mathematically by the equation: F = ma, where F (in Newtons) is the net force applied to an object, m (in kg) is the mass of the object, and a (in m/s 2) is the acceleration of the object. If the net force on an object is zero, then its acceleration is zero, which means that the object does not accelerate but remains in motion at a constant speed.
• Newton's third law, also called the law of action and reaction, states that for every action there is an equal and opposite reaction. This means that if one body exerts a force on another body, the latter exerts an equal and opposite force on the first body.

What is F = ma for?
Newton's laws describe how objects move in response to forces acting on them. They make it possible to understand how objects move, turn, accelerate and slow down but also how objects will move in the future according to the forces acting on them.

Cette loi fait le lien entre la force et le mouvement. Souvent on souhaite faire le lien entre la force et la vitesse (quelle force dois-je appliquer pour atteindre telle vitesse ?). C'est utile dans de nombreux domaines, tels que l’aérospatiale, la robotique, la gravité, la dynamique des fluides, l'électromagnétisme, l'optique, etc.

Example of calculation
Suppose an object has a mass of 1 kg and a constant force of 1 N is applied to it. According to Newton's second law (F = ma), force is equal to mass multiplied by acceleration.
Thus, we can use the formula F = ma to calculate the acceleration of the object: 1 N = 1 kg x a
Thus, we have: a = 1 N / 1 kg ⇒ a = 1 m/s²
The force of 1 N applied to the 1 kg object produces an acceleration of 1 m/s².
More specifically, this means that the object gains a speed of 1 meter per second for every second it moves. For example, if the object was stationary initially, after one second of applying the force of 1 N it would move at a speed of 1 m/s, after two seconds it would move at a speed of 2 m /s, after three seconds it would move at a speed of 3 m/s, and so on.

note: a newton (symbol N) is a unit of measurement derived from the international system (SI) which measures force. It is defined as the force required to accelerate a 1 kilogram mass to an acceleration of 1 meter per second squared (1 m/s²).
In other words, 10 N represents a force which is capable of producing an acceleration of 1 m/s² on an object of mass 10 kg. But also, 10 N represents a force capable of producing an acceleration of 10 m/s² on an object of mass 1 kg. 1 m/s represents a speed of 3.6 km/h (about the speed of walking).

### Image: F = ma, where F (in Newton) is the net force applied to an object, m (in kg) is the mass of the object, and a (in m/s2) is the acceleration of the object . To reach a speed of 36 km/h (10 m/s) in 1 second, a car weighing 1 ton (1000 kg) must be pushed by a force of F = 1000 x 10 N. But to reach a speed of 36 km/h in 10 seconds the force will be F = 1000 x 1 N.

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