# Newton's first law of motion/inertia with examples and definition

Newton, the father of physics established the laws of motion in his book "Principia" in 1687.

The SI unit for measuring the force is Newton.

## Definition of Newton's first law of motion

Every body maintains its initial state of rest or motion with uniform speed on a straight line unless an external force acts on it.

in other words, If the sum of all the forces acting on a particle is Zero then and only then the particle remains unaccelerated.

The first law is also called the law of Galileo or the law of Inertia.

# Formula for newton's first law of motion

According to newton's first law of motion, if the net force acting on an object is Zero, then the acceleration of that object will be zero. i.e.,

Force=Mass * Acceleration
F= M*A
if F=0,then after putting value of F in above equation
0=M*A
0/M=A
0=A or A=0

## Inertia

Inertia is the property of a body by virtue of which the body opposes a change in its initial state of rest or motion with uniform speed on a straight line.

Inertia is of two types

1. Inertia of rest
2. Inertia of motion

## Examples of the first law of motion/Inertia:

1. When a car or bus starts suddenly, the passengers bends backwards.
2. when a running horse stops suddenly, the rider bends forward.
3. when a coat/blanket is beaten by a stick, the dust particles are removed.
The first law gives the definition of force.

## Concept of Newton's first law of motion:

If the sum of all the forces on a given particle is F and its acceleration is A, the above statement may also be written as

" A=0 if and only if F=0"

Thus, If the sum of all the forces acting on a particle is known to be zero, we can be sure that the particle is unaccelerated, or if we know that a particle is unaccelerated, we can be sure that the sum of the forces acting on the particle is Zero.

However, the concept of rest, motion or acceleration is meaningful only when a frame of reference is specified. Also, the acceleration of the particle is, in general, different when measured from different frames. Is it possible then, that the first law is valid in all frames of reference?

for example, An elevator cabin falls down after the cable breaks. The Cabin and all the bodies fixed in the cabin are accelerated concerning the Earth and the acceleration is about 9.8 m/s2 in the downward direction.

Consider the land in the cabin. The force acting on the lamp are (a) the gravitational force w by the earth and (b) the electromagnetic force ( T) tension by the rope. The direction of w is downward and the direction of T is upward. The sum is (W - T) downward.

Measure the acceleration of the lamp from the frame of reference of the cabin. The lamp is at rest. The acceleration of the lamp is zero. The person A who measured this acceleration is a learned one and uses Newton's first law to conclude that the sum of the force acting on the particle is zero, i.e.

W - T =0 or, W = T.

Instead, if we measure the acceleration from the ground, the lamp has an acceleration of 9.8m/s2. Thus, a ≠ 0 and hence the person be who measured this acceleration, concludes from Newton's first law that the sum of the forces is not zero. Thus, W - T  ≠ 0 or W  ≠ T.

If A measures acceleration and applies the first law he gets W = T. If B measures acceleration and applies the same first law, he gets, W ≠ T. Both of them cannot be correct simultaneously as W and T can be either equal or unequal. At least one of the two frames is a bed frame and one should not apply the first law in that frame.

There are some frames of reference in which Newton's first law is valid. Measure acceleration from such a frame and you are allowed to say that " a = 0 if and only if f = 0". But there are frames in which Newton's first law is not valid. You may find that even if the sum of the forces is not zero, the acceleration is still zero. Or you may find that the sum of the forces is zero, get the particle is accelerated. So the validity of Newton's first law depends on the frame of reference from which the observer measures the state of rest, motion and acceleration of the particle.

## There are are two types of frame of reference

A frame of reference in which Newton's first law is valid is called an inertial frame of reference. If frame in which Newton's first law is not valid is called a non-inertial frame of reference.

## Inertial frames other than earth

Suppose S is an inertial frame and S' is a frame moving uniformly with respect to S. Consider a particle P having acceleration aps with respect to S and aps' with respect to S'.

We know that,

aps = aps'+as,s

as S' moves uniformly with respect to S,

as',s = 0.

ap,s = ap,s'........... (i)

now, S is an inertial frame. So from definition, ap,s = 0, if and only if F = 0 and hence, from (i), ap,s' = 0 if and only if F = 0.

Thus, S' is also an inertial frame. We arrived at an important result:

All frames moving uniformly with respect to an inertial frame are themselves inertial.

Thus, train moving with uniform velocity with respect to the ground, plane flying with uniform velocity with respect to a highway, etc., are examples of inertial frames. The sum of the forces acting on a suitcase kept on the shelf of a ship sailing smoothly and uniformly on a calm sea is zero.