Laws of Motion

Matter and motion are two inseparable fundamental concepts. Matter in motion and the force that brings about the motion are linked together by three celebrated laws known as Newton’s Laws of Motion, after the great mathematician, Sir Isaac Newton. These laws are basically true in the case of bodies moving with speeds less than that of light.

Newton’s First Law of Motion

“Everybody continues in its state of rest or of uniform motion in a straight line, unless an external force is applied on it.” 
This law gives the qualitative definition of force. A body can change its state (rest or motion) only when some external force is applied.

This law embodies two aspects; property of inertia and definition of force.

Property of Inertia

Objects at rest shows no tendency to move by itself, and, similarly an object, already in motion, continues to move in a straight line. This inability of the body to change its state is called inertia.

On the basis of rest or motion, inertia can be;
1. inertia of rest
2. inertia of motion
3. inertia of direction
Illustration
a. A coin placed in a cardboard covering a glass falls into the glass when the glass is pulled suddenly. It is because before pulling the cardboard both the cardboard and the coin are in rest. When the cardboard is pulled, the cardboard comes into motion, while the coin tends to remain at rest due to inertia of rest. So, the coin falls into the glass.

b. A man getting out of a moving bus run in the same direction for certain distance. It is because when the man steps down from bus, his feet come to rest while the upper part of his body tends to remain in motion due to inertia of motion and he falls in forward direction. To prevent this, the man should run in the same direction for certain distance.

c. When a moving bus takes a turn, its passengers also fall in opposite direction to which the bus has taken the turn. It is because of inertia of direction.

Examples mentioned above shows us that material objects possess certain amounts of inertia. The question how large or how little is the amount of inertia in a given body gives rise to the important notion of ‘mass’.

Definition of Force

As explained earlier, due to inertia, a body has no tendency of its own to change its state of rest or uniform motion. A force is always necessary to cause any change in the original state (either rest or uniform motion) of a body. Hence, force may be defined in the following way;
A force is that which acting on a body changes or tends to change the state of rest or of uniform motion of the body.

Newton’s Second Law of Motion

“Force acting on a body is directly proportional to the time rate of change of momentum.” 
Let force $F$ act on a body having momentum $P$. Then, according to Newton’s second law of motion, Force $∝$Time rate of change of momentum. \[\therefore F ∝\frac{dP}{dt}\] \[F=k\frac{dP}{dt}\] where, $k$ is proportionality constant and $k=1$. \[∴F=\frac{dP}{dt}\] This law gives the quantitative definition of force.

Measurement of force

From second law, \[F=\frac{dP}{dt}\] If the body has mass $m$ and velocity $v$, then, \[F=\frac{d(mv)}{dt}\] \[F=m\frac{dv}{dt}+v\frac{dm}{dt}\] \[F=m\frac{dv}{dt}\] \[\text{here, } a=\frac{dv}{dt}\] \[∴F=ma\] Force is a vector quantity and its SI unit is $\text{Newton}$ $(N)$.

The magnitude of a force may be defined as the number of units in the given force. Its direction is the direction of acceleration produced by it.
The force is completely known if its;

  1. Point of application
  2. Magnitude, and
  3. Direction

are known.

Once a force is completely known, it can be geometrically represented by straight line segment;

  1. Drawn through the point representing the point of application.
  2. Drawn in the direction pointing the direction of force, and,
  3. Drawn so that the length of the line segment is proportional to the magnitude of the force.

[Know more: Force]

Newton’s Third Law of Motion

We know that every objects have mass. Mass being a measure of the inertia of the object, is inseparable with the force associated with it. If we have two objects, the forces associated with the masses of the objects mutually interact. These two interacting forces are called ‘action‘ and ‘reaction‘. If we call one of them action, the other is called its reaction. Action and reaction act on different objects.
Newton’s third law involves action and reaction on objects and is stated as;

“In every action, there is an equal and opposite reaction.” 

Let a body $A$ exerts a force $F_1$ on body $B$ and then, the body exerts force $F_2$ on body $A$, Then, according to Newton’s third law of motion, \[F_1=-F_2\] 

Illustration
a. We move by pressing the ground backward with our foot. The ground gives us equal and opposite force which enables us to walk. 
b. When a balloon filled with air and its mouth downward is released, it moves upward. Because when the mouth is released, the air escapes out with high velocity and the balloon experiences an equal and opposite force in upward direction.


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