A non inertial Frame of Reference is the frame of reference which is having acceleration($a_{0}$) Example Free Falling elevator

Newtons law are valid in inertial frame of reference only. We cannot apply them as it is in non inertial frame of reference as it left out the acceleration of the object because of the frame of reference. We have to add fictitious force to make them valid

Let me provide simple fictitious force examples to illustrate this.

a)You are moving in car which is accelerating. From your frame of reference,a block on the road would be accelerating in opposite direction.

Now if we apply newton’s law, we will find acceleration to be zero as no net force is acting. But the block has acceleration from car frame of reference.

So to fix this issue,we will add one fictitous quantity in the Newton law equation like

$F=F_{0}+ma$

Where $F_0$ is the fictitous force and it is in opposite direction of accleration frame

$F_{0}=-Ma_{0}$

Where $a_{0}$is the acceleration of Non inertial frame of refrence

(b) Now let me further illustrate this with example of free falling elevator

A free falling elevator is an non inertial frame of reference. The acceleration of the elevator as defined from the observer on the ground will be

g=-g**k**

Where **k** is the unit vector along vertical axis in the upward direction

Let us take an unattached object of mass M in the elevator.

From the frame of refrence of free falling elevator,Two forces are acting on the mass

Fictitous Force due to non inertail frame of refrence

$F_{fic}=Mg$

It is opposite to the acceleration of the elevator

Gravitational Force on the Mass

$F_{G}=-Mg\mathbf{k}$

So the total Force on the body from elevator frame of reference

$F_{T}=F_{fic}+F_{G}=0$

Which mean body is unacclerated in the elevator frame of refrence. The body will appear to be suspended in the air ,if it has no initial relative velocity to the elevator

(c) A rotating merry go round is a non inertial frame of reference.

The acceleration of the person sitting in merry go round as defined from the observer on the ground will be

$a=\frac {mv^2}{r} \mathbf{r}$

The direction is radially inwards

Now the person is at rest in the rotating frame of reference, so net force should be zero. If $\mathbf{F}_{fict}$ is the fictitious force from the rotating merry go round non inertial frame of reference ,then

$\mathbf{F}_{fict} + m \frac {mv^2}{r}\mathbf{r} =0$

or

$\mathbf{F}_{fict}=-m \frac {mv^2}{r}\mathbf{r}$

It will be radially outward

Few more important things about Fictitious force

- Fictitous force are called pseudo force.
- It simple represent the effect of the acceleration of the non inertial frame of refrence
- They dont have any physical significance
- Whenever we work the problem in non inertial frame of refrence,always make sure to include fictitous force in the newton law

Hope you like this post on fictitious force examples

**Also Reads**

Dimension of force

How to solve kinematics Problems

work done by Multiple Forces

https://en.wikipedia.org/wiki/Fictitious_force