# Newton’s Laws of Motion

Learning Objectives
On completion of this lesson, you will be able to learn-
• Newton’s first law of motion
• Newton’s second law of motion
• Newton’s third law of motion.
Newton's three laws of motion give the fundamental properties of force and the relationship between force and acceleration. The first of these laws describe the natural state of motion of a body on which no external forces are acting, whereas the other two laws deal with the behavior of bodies under the influence of external forces.

## Newton’s First Law

Newton’s First Law summarizes experiments and observations on the motion of bodies on which no external forces are acting, thus the first law is -

A body at rest remains at rest, and a body in motion continues to move at a constant velocity unless acted upon by an external force.

The tendency of a body to continue in its initial state of motion (a state of rest or a state of uniform velocity) is called its inertia.

Accordingly, the First Law is often called the law of inertia.

## Newton’s Second Law

Newton’s Second Law of motion establishes the relationship between the force acting on a body and the acceleration caused by this force.
Newton’s Second Law states:

The external force acting on a body gives it an acceleration that acts in the direction of the force and has a magnitude directly proportional to the magnitude of the force and inversely proportional to the mass of the body.

If we denote acceleration by a force F and mass by m then the second law of motion is given as -
a = F/m .......(1)
or,
ma = F ........(2)
According to Eq. (1), the acceleration vector equals the force vector divided by the mass. Thus, this equation specifies both the magnitude and the direction of the acceleration.

The definition of force also relies on the Second Law. To measure a given force say, the force generated by a spring that has been stretched a certain amount; we apply this force to the standard kilogram. If the resulting acceleration of the standard kilogram is a, then the force has a magnitude

F = ma = 1 kg × a ......(3)

In the metric system of units, the unit of force is the Newton (N). This is the force that will give a mass of 1 kg an acceleration of 1 m/s2,

1 Newton = 1N = kg.m/s2 ..........(4)

In the metric system, the unit of acceleration is m/s2, and the unit of mass is the kilogram (Kg). In CGS system unit of force is Dyne (D).

1N = 10D .......(5)

## Newton’s Third Law

When you push with your hand against a table or wall, you can feel the wall pushing back at you. Thus, the mutual interaction of your hand and the wall involves two forces; the “action” force of the hand on the wall and the “reaction” force of the wall on the hand. The important point is that forces always occur in pairs; each of them cannot exist without the other.

Newton’s Third Law gives the quantitative relationship between the action force and the reaction force.

Whenever a body exerts a force on another body, the later exerts a force of equal magnitude and opposite direction on the former.

This is sometimes stated, to every action, there is an equal and opposite reaction. For instance, if the push of your hand on the wall has a magnitude of 60N, then the push of the wall on your hand also has a magnitude of 60N.

This equality of the magnitudes of action and reaction holds even if the body you push against is not held in a fixed position (like a wall), but is free to move. Thus, if you push on a cart with a force of 60 N, the cart will push back on you with a force of 60 N. Note that although these action and reaction forces are of equal magnitudes, they act on different bodies and their effects are quite different: the first force gives acceleration to the cart, whereas the second force merely slows your hand and prevents it from accelerating as much as it would if the cart were not there. Thus, although action and reaction are forces of equal magnitudes and of opposite directions, their effects
do not cancel because they are acting on different bodies.
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