The concepts invoked in “Newton’s Laws of Motion” (mass, velocity, momentum, force) have predecessors in earlier work, and the content of Newtonian Physics was further developed after Newton’s time. Newton combined knowledge of celestial motions with the study of events on Earth and showed that one theory of mechanics could encompass both.

Sir Isaac Newton is known as the “Father of Physics” and also announced as “The Scientist of the Millennium” for his numerous groundbreaking universal concepts.

Newton’s laws of motion are three basic laws of classical mechanics that describe the relationship between the motion of an object and the forces acting on it. These laws can be paraphrased as follows:

1. A body remains at rest, or in motion at a constant speed in a straight line, unless acted upon by a force.
2. When a body is acted upon by a force, the time rate of change of its momentum equals the force.
3. If two bodies exert forces on each other, these forces have the same magnitude but in opposite directions. 

The three laws were first stated by Isaac Newton in his Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy), originally published in 1687. Newton used them to investigate and explain the motion of many physical objects and systems, which laid the foundation for classical mechanics. 

Newton’s First Law of Motion

Newton’s first law reads,

Every body continues in its state of rest, or of uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it.

The modern understanding of Newton’s first law is that no inertial observer is privileged over any other. The concept of an inertial observer makes quantitative the everyday idea of feeling no effects of motion. The principle expressed by Newton’s first law is that there is no way to say which inertial observer is “really” moving and which is “really” standing still. 

Newton’s Second Law of Motion

Newton’s second law reads,

The change of motion of an object is proportional to the force impressed; and is made in the direction of the straight line in which the force is impressed.

By “motion”, Newton meant the quantity now called momentum, which depends upon the amount of matter contained in a body, the speed at which that body is moving, and the direction in which it is moving. In modern notation, the momentum of a body is the product of its mass and its velocity. Newton’s second law, in modern form, states that the time derivative of the momentum is the force.

The law is sometimes presented as a definition of force – the force equals the product of the mass and the time derivative of the velocity, which is the acceleration:  F = ma

Newton’s Third Law of Motion

Newton’s third law reads,

To every action, there is always opposed an equal reaction; or, the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

Newton’s third law relates to a more fundamental principle, the conservation of momentum. The latter remains true even in cases where Newton’s statement does not, for instance when force fields, as well as material bodies, carry momentum, and when momentum is defined properly, in quantum mechanics as well.

Newton’s Zeroth Law

There are several hidden assumptions present in the Newtonian synthesis, One of these was stated as Newton’s Zeroth Law. It is called the “zeroth” law because it came to light after the first and second laws of thermodynamics had already been established and named, but was considered more fundamental and thus was given a lower number — zero. 

The zeroth law states that: if two thermodynamic systems are in thermal equilibrium with each other, and also separately in thermal equilibrium with a third system, then the three systems are in thermal equilibrium with each other.

Applications of The Newton’s Law of Motion

Newton’s three laws are the basis for mechanics. The study of the motion of objects and the forces acting on them is called Mechanics. It is a significant branch of physics and has applications in engineering and technology. 

For example, the design of vehicles, spacecraft, and their control of them are all based on these three laws.

Applications of the First Law of Motion

1. Newton’s first law expresses the principle of inertia: the natural behavior of a body is to move in a straight line at a constant speed. In the absence of outside influences, a body’s motion preserves the status quo. 
2. An athlete continues to run for some time, even after reaching the finishing line. This is because they cannot stop suddenly due to inertia.
3. A switched-off fan will continue to move for some time till friction stops it.
4. An application of using the first law is in car safety equipment like seatbelts and airbags. When there is a crash or sudden braking of the car, the passengers are pushed forward. The top part of their bodies is still at the same velocity as that of the car before the crash and continues to move forward due to inertia. The seatbelt prevents them from lunging forward. An airbag inflates quickly in case of a crash and prevents the driver or passenger in the next seat from hitting the dashboard.

Applications of the Second Law of Motion

1. Newton’s second law has also been regarded as setting out a research program for physics
2. Establishing important goals of the subject to identify the forces present in nature and to catalog the constituents of matter.
3. A ball kicked with a stronger force moves farther distance due to higher acceleration.
4. Pushing a heavy object requires more force to be applied due to higher mass.
5. An application of using the second law is in designing fighter jets. Fighter jets need to quickly turn around to dodge artillery fire from the ground or enemy planes. Jets with lighter mass are easy to turn around quickly with lesser force than those with heavier mass due to inertia.

Applications of Third Law of Motion

1. We see examples of the third law every day. For example, while walking, we push the ground back. This causes our body to move forward.
2. While swimming, we push the water back, making our body move forward.
3. Birds push down the air with their wings causing them to stay up in the air and move forward.
4. A gun recoils while firing. It means that the gun is pushed back when the bullet is fired at high speed.
5. Rockets are an excellent example of the application of the third law. The thrust of high-pressure gases by burning fuel from the engines pushes the rockets up with a very high velocity, enough to escape the earth’s gravitational force.

Limitations to Newton’s laws:

• New theories are necessary when objects move at very high speeds (special relativity), are very massive (general relativity), or are very small (quantum mechanics).
• Newton’s laws are not valid in a non-inertial frame or object is moving with uniform acceleration. 
• Not applicable in a non-inertial (accelerated) frame of reference. 
• Newton’s laws are only applicable to point objects and to rigid bodies.
• Results obtained by applying Newton’s laws of motion for objects moving with speeds comparable to that of light do not match with the experimental results and Einstein’s special theory of relativity has to be used. 
• Newton’s laws of motion fail to explain the behavior and interaction of objects having atomic or molecular sizes, and quantum mechanics has to be used.

The laws were not applicable under various circumstances, however, scientists like Max Kepler and Robert Hook made further observations and gave new theories that could fit scientifically. 

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