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Define inertial and non-inertial frames of reference. Give examples.

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Hint:The quantities such as velocity, displacement and acceleration are all dependent on frame. Frame of reference consists of an abstract coordinate system. This consists of a set of reference points that uniquely fix the coordinate system and standardize measurements within that frame. Inertial frame implies the reference under the effect of inertial while non-inertial frame implies the reference is free of inertial.

Complete answer:
As discussed in the hint, there are two types of frame of reference, they are:
-Inertial Frame of Reference
-Non-inertial Frame of Reference

Inertial Frame of Reference: Frames in which Newton's law holds true are called inertial frame of reference. Newton’s first law states that if no external force is acting on a body it will stay at rest or remain in uniform motion. The term inertial frame is relative as we have to assume a reference frame to be the inertial frame of reference. A more general definition of an inertial frame is, Inertial frame is at rest or moves with constant velocity with respect to my assumed inertial frame of reference. For example: A car moving with constant velocity when an observer is on the road.

Non-inertial Frame of Reference: A non-inertial frame of reference is one that is accelerated with respect to the assumed inertial frame of reference. If a body does not obey the rules of inertial frame of reference it can be said to be in a non-inertial frame of reference. Newton’s first law of motion does not hold true in a non-inertial frame of reference. The acceleration of the system in a non-inertial frame is taken with respect to an inertial frame of reference. An example of a non-inertial frame of reference is the Coriolis force and centrifugal force.

Note: In simple terms, the inertial frame of reference is one in which Newton’s laws of motion are applicable. Any system having constant velocity or at rest is an example of an inertial frame of reference. On the other hand, when Newton's laws of motion are not applicable then such a system is said to be in a non-inertial frame.