What are Newton's Laws?

Formula for Newton's Second Law of Motion.
Formula for Newton's Second Law of Motion.

Newton’s famous laws of motion are three in number. These laws laid the foundations for Newtonian mechanics, otherwise known as classical mechanics. Newtonian mechanics is a field that is focused on the set of laws that govern the behavior of an object after forces act on that object.

Newton’s Laws of Motion

These three laws have been written in many different forms over the centuries, at least three, but they can be expressed briefly as follows:

The first law states that an object either remains static or will continue to move at a constant speed unless it is influenced by another force. This law assumes that an object is in an inertial frame of reference. An inertial frame of reference is one in which the forces acting on a body, whether static or stationary, have a net force of zero. This frame means that this body will remain stationary or keep moving at a constant velocity.

The second law also assumes that an object is in an inertial frame of reference. The law states that the vector total of the forces (denoted by F) on a body is equivalent to the product of the mass (denoted by m) of that body and its acceleration (denoted by a). Mathematically put, this means that: F = m*a. Another assumption to keep in mind is that mass does not change.

The third law of motion is more widely known. When one entity exerts a force (F) on another object, then the second body will also push back with a force that’s equal to F. With every action, there is an equal and opposite reaction.

History and Overview

The three laws motion were initially put together by none other than Isaac Newton, hence the name Newton’s Laws of Motion. Newton first wrote the rules governing motion in the year 1687 in his release, Mathematical Principles of Natural Philosophy (Philosophiæ Naturalis Principia Mathematica in Latin).

Isaac Newton sought to explain why objects behave as they do while in motion or why they stay the way that they do, that is, while motionless. Consequently, he used the laws together with other of his laws to explain the motion of systems as well as physical objects.

Another critical thing about Newton’s laws is that they are applicable for objects that are considered single point masses. This term means that an object’s shape and size are ignored so that focus can be on its motion. This view is applicable if the objects are small in comparison to the distances that are involved while it’s being analyzed. This way allows for any object, regardless of size, to be conceptualized as a particle to be analyzed.

As stated earlier, the three laws are not enough to explain the motion behavior of all objects. For example, he could not explain Kepler’s laws of planetary motion until he combined his laws of motion with another of his law called the law of universal gravitation. These laws also cannot be used to explain the movement of deformable and rigid bodies. In fact, it was in the year 1750 that Leonhard Euler generalized Newton’s motion laws so that they could be applied to the rigid and deformable objects as well supposed as a continuum. In Euler’s laws, which can be derived from the original Newton’s laws, an object is presumed to be a collection of discrete particles that are each governed by Newton’s laws. However, Euler’s laws can be assumed to be axioms that describe the motion laws for extended entities, independent of the structure of the particles.

As previously stated, Newton's laws are only applicable to a set of frames called the inertial reference frames, which are sometimes called Newtonian frames of reference. However, there has been some debate among scholars concerning the first and the second laws. One school of thought argues that the first Newton law outlines what an inertial frame of reference is and so the second law is true if, and only if, it is observed from an inertial frame of a reference point of view. When all these factors are considered, it is impossible to determine the special of the two laws. The other school of thought argues that the first law is a consequence of the second one.

Another aspect of these laws to keep in mind is that special relativity has outmoded Newtonian laws. That is not to mean that they are useless. The laws are suitable for approximating the behavior of moving objects when their speeds are below that of light.

The Three Laws in Detail

The First Law

Newton’s first law states that the velocity of an object in motion shall remain constant if the net force is zero. In this case, force refers to the vector summation of all forces that are affecting that body. Velocity is a vector quantity since it shows the speed of the body as well as its direction of motion. This is to mean that constant velocity describes a constant direction and speed of the object.

To put it in terms of a mathematical formula, it becomes: ∑F = 0 ↔ dv/dt = 0. In the formula, v represents the velocity while t represents time taken. The formula only proves that an object that is motionless will remain that way unless affected by a force, and a body that is moving will not alter its velocity unless influenced by a force. This kind of motion is called uniform motion. A good way to demonstrate this is through the tablecloth experiment. Dishes placed on top of the tablecloth will remain as they are when the tablecloth is removed skilfully and fast. It is not a trick but Newton’s laws in action. A moving object’s natural tendency is to stay as it is. If someone wants to alter this tendency, then force must be applied on that object. This law also sets forth the reference frames for the other two laws.

The Second Law

A different way of stating the second law is the rate of change of the momentum of an object in direct relation to the amount of force that is applied. Also, this change of its momentum occurs in the same direction of the force applied.

Mathematically, it can be expressed as F = dp/dt = d (mv)/dt. The p is a product of mass (m) and velocity (v) whereas the t represents the time taken. The formula is one way of expressing this, however it is also possible to express it in terms of acceleration of the object. In the stating of the laws, it is assumed that mass is constant. Therefore, it’s not necessary to include it in the differentiation formula. Therefore, it becomes: F = m (dv/dt). Since velocity (v) divided by time (t) provides the acceleration, the formula now becomes F = m * a.

Mass gained or lost by the entity will also affect the momentum of the object which would not be a consequence of an outside force and a different equation becomes necessary. Also, at higher speeds, the calculation that the product of the object’s mass at rest and its speed is inaccurate.


Impulses (J) take place when a force (F) acts on an object over a time interval (Δt) as its mathematical expression is much closer to Newton’s wording of his second law. The concept of impulse is mostly utilised while analysing collisions. Mathematically it becomes: J = Δp = m* Δv.

For systems of variable mass, say a rocket that is combusting fuel, the second law cannot be applied because they are open. As such, making its mass a function of its time is incorrect.

Newton’s Third Law

The last law of motion states that all forces that exist amongst two bodies do so with equal magnitude and in opposing directions. For instance, if an object 1 exerts a force of magnitude F₁ on another body 2, then Newton’s third law states that object 2 shall exert a force of magnitude -F₁, such that F₁ = - F₁. The resulting total force equates to zero. That is, F₁ + (- F₁) = 0.

This law shows that all the forces generated are a direct consequence of interaction between different bodies. It also shows that a force cannot exist without its equal and opposite equivalent to cancel it out. The direction and magnitude of the force may be determined by one of the forces. For example, object 1 may be the one exerting force and so it is called the “action” force with the force from object 2 called the “reaction” force. These two names are why the third law is sometimes called the “action–reaction” law. However, at times it is impossible to ascertain which one of the two forces is the action and which one is the reaction. It is impossible for one force to exist without the other. A practical example of this is when someone is walking. They push against the earth, and the earth pushes back.


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