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**Are Newton's Laws of motion universally applicable?**

Newtonian mechanics can be used to explain the dynamics of a particle in most of the real life cases, however in some cases where the reference frame in consideration is accelerating with some finite acceleration, the Laws of Motion cannot be directly applied.

Ex: Consider the case of a pendulum bob suspended inside a car accelerating with acceleration a.

For a stationary observer the bob is seen to accelerate with the same acceleration as a.

In the inertial frame, the net forces acting on the bob are:

- Weight, $F_{g} =mg$
- Tension, $T$

Applying Newton's Second Law of motion,

$∑F_{g} +T=0$

In component form it can be written as,

$∑F_{x}=Tsinθ=ma$

$∑F_{y}=Tcosθ−mg=0$

Hence for a stationary observer the bob seems to be accelerating along with the car and Newton's Laws are valid. However in the reference frame of the car, the bob is stationary and there should be no net force acting on it.

$∑F=0$ , (Car's reference frame)

This can only happen if we assume an extra inertial force acting on the bob.

$∑F_{g} +T+F_{I} =0$

$∑ma+F_{I} =0$

$F_{I} =−ma$

The free body diagram of the bob in the frame of reference of the car is

Thus, we have seen that

**the newton's second law isn't valid in the non inertial frame, unless we consider the inertial force on the object in consideration. This force is also called "pseudo force" or fictitious force as it has no existence in the inertial frame.**