**Newton’s laws of motion –**

Newton’s laws of motion are physical laws that are the basis of classical mechanics. These laws explain the relationship between the force acting on an object and the motion of that object resulting from it. These have been expressed in many ways over the three centuries. Newton’s three laws of motion, traditionally, are summarized as follows:

**• First law: **Everybody remains in its state of rest or in a state of uniform motion in a straight line until an external force forces it to do so. It is also called a rule.

**• Second Law:** The rate of change of momentum of anybody is proportional to the applied force and its (momentum change) direction is the same as that of the force.

F ∝ (mv – mu)/t

F ∝ (m(v – u))/t

F ∝ ma

F = ma

F = force, Newton (N) or (kg. m/s 2 )

M = mass (kg)

A = acceleration (m.s -2)

**• Third Law: **For every action, there is always an equal and opposite reaction.

Newton first compiled them in his book Philosophiae Naturalis Principia Mathematica (1678). Newton used them in many places in the explanation of problems related to the motion of physical objects. In the third part of his treatise, Newton showed that these three laws of motion and their law of universal gravitation together are able to explain Kepler’s law related to the motion of celestial bodies.

**Overview – **

Newton’s laws of motion are applied only to those objects which we can consider a particle. Meaning that while measuring the speed of those objects, their size is ignored. These rules are applied considering the body of those objects as centred in a point. This is done when the distances are very large compared to the objects in the analysis. Therefore, considering the planets as a single particle, their orbital motion can be measured.

In their original form, these laws of motion cannot be applied to rigid and deformable bodies. In 1750, Leonard Euler extended Newton’s laws of motion and formulated Euler’s laws of motion, which can be applied to rigid and deformable bodies. Euler’s laws of motion can be derived from Newton’s laws of motion if an object is considered to be an assembly of discrete particles to which Newton’s laws of motion can be applied individually.

Newton’s laws of motion also apply only in some reference systems, which are called inertial reference systems. Many authors believe that the first law defines the inertial frame of reference and the second law is valid only in those frames of reference, for this reason, the first law cannot be called a special form of the second law. But some consider the first law to be a consequence of the second. A clear concept of reference frames developed long after Newton’s death.

**Why are the laws of motion important? –**

Newton’s laws are essential because they relate to everything we do or see in everyday life. These laws tell us how things move or stay still, why we don’t float out of our beds or fall through the floor of our house.

**First rule – **

**Definition:**

“Every object remains in its state of rest or uniform velocity until it is induced to change its state by some external factor (force).”

In other words, an object at rest will remain at rest and an object in motion will remain in motion unless an external force is applied to it.

Newton’s first law defines inertia, as a natural property of matter that resists change in motion. That’s why the first law is also called the law of inertia. This law also indirectly defines the inertial frame of reference (the frame of reference in which the other two laws are valid) and forces. Due to this, this law was kept first by Newton.

This rule does not apply in any arbitrary frame. This law applies only in a special type of frame, known as an “inertial frame”. Therefore, the inertial frame is the frame in which Newton’s first law applies. Any frame moving with constant velocity with respect to an inertial frame is an inertial frame.

Simple verification of this law is difficult because most bodies feel the effects of friction and gravity.

In fact, Galileo described this observation before Newton. Newton expressed it in other words.

**Second rule – **

**Definition : **

“The change in momentum of an object is directly proportional to the force exerted on that object and occurs in the same direction."

The following points can be derived from Newton’s law:

F = dp/dt,

Where F’ is the force, p is the momentum and t is the time. According to this equation, when there is no external force acting on a body, the momentum of the body remains constant.

When the mass of the object is constant, the equation can be written in a simpler form:

F = m

Where m is the mass and a` is the acceleration.

That is, the force applied to an object is proportional to the acceleration of that object.

**Impulse – **

Impulse second law is related to a`.

Impulse means a change in momentum. In other words:

I = ∆p = m∆v

Where I am the impulse. Impulse is very important in the analysis of collisions. Let the mass of a body be m. On applying a law force F on it for ∆ t time interval, ∆v changes in velocity. Then Newton –

F = ma = m.∆v/∆t

F∆t = m∆v. m∆v = ∆p

F∆t = ∆p

Hence, the impulse given to a body is equal to the change in momentum produced in the body. Hence, the unit of impulse is the same as that of momentum (Newton-second).

The third law means that for any force there is a corresponding force which is equal and opposite. Newton used this law to describe the law of conservation of momentum, but in reality conservation of momentum is a more fundamental principle. There are many examples in which momentum is conserved but the third law is not valid.

By Chanchal Sailani | January 04, 2023, | Editor at Gurugrah_Blogs.

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