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Inertial and Non-Inertial Frame of Reference - JEE Important Topic

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Last updated date: 19th May 2024
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What is a Frame of Reference?

In Physics and Astronomy, a reference frame refers to an abstract coordinate system whose direction, origin, and scale are specified by a set of geometric reference points. The frame of reference has physical reference points that uniquely fix the coordinate system and standardise measurements within that frame of reference. In this article, we will have a deep insight into the concept of reference frames, the types of reference frames, and the difference between inertial and non-reference frames of reference.


Types of Frame of Reference

According to Newton's law, if an object has a net force of zero, its acceleration will also be zero. In this case, the body may be stationary or evenly moving with a constant velocity vector. A different frame of reference was observed. A reference frame in which the first law of motion is valid and the coordinate system that can be directly applied is known as the inertial system. Moreover, reference frames to which Newton's first reference law does not apply directly are non-inertial reference frames.


Thus, the frame of reference is widely differentiated into two types:

  • Inertial reference frame

  • Non-inertial reference frame

Example of Frame of Reference

Before we start with other frames of reference, we will first understand the concept of the frame of reference with a few examples. 

  • Let's say, a train is running and a person is sitting on the train and looking at a tree passing by. In this case, the train is in the frame of reference and the tree appears to be moving.

  • If you think about the opposite, people on the platform consider the tree to be a stationary object. It will be his or her reference frame. These two observations are correct, but they differ because of the different reference frames.

  • When you see the ball rolling on the road, whatever is on the side of the road or on the ground, you can say that the ball is moving because the frame of reference is on the road. All motion measurements are compared to the reference frame. Therefore, the best example of a frame of reference is the earth, even if it is constantly moving.

  • A person sitting on the earth is stationary with respect to the earth's frame of reference while moving against the moon. Therefore, if the earth is the reference system, the moon accelerates with respect to the earth and becomes a non-inertial frame of reference.

Inertial Frame of Reference

Now, let us understand the inertial frame of reference in detail. The following section provides a detailed description for the inertial frame of reference.

  • Assuming the body is held on the surface of the planet, it is stationary for humans on Earth, but moving for humans on the Moon. Is there an inertial coordinate system from Earth?

  • An inertial frame of reference is a coordinate system that is considered to reflect the inertial coordinate system defined by the term inertial coordinate system. 

  • By a more general definition, an inertial frame is either stationary or moving at a constant velocity around an imaginary inertial coordinate system, depending on the context.

  • The reference frame is basically part of the surrounding environment used to measure the movement of the moving object. The world around us appears to be stationary, and it must be uniform, as any movement we measure with respect to our surroundings is properly observed.

  • Railcars move in orbit, so the movement of all objects we see is not accurately measured, but instead is as inaccurate as the movement of railcars. Is the observation of moving objects unaffected by this factor?

  • If a moving object moves unevenly due to the force acting in the real world, it will move unevenly even in the reference coordinate system of the moving railroad vehicle by the amount that exactly corresponds to the force acting in the real world.

  • A coordinate system that moves constantly, like a train, does not affect the laws of motion. It was first proposed by Galileo Galilei decades before Newton announced the Law of Motion. Galileo's statement includes all the laws of nature, not just Newton's rules.

  • If Newton's law of motion is valid in the real world, then the law of inertia is correct in all reference systems that move exactly and evenly around a common world. Whenever it is in such a frame, it is called an inertial frame.

Example of Inertial Frame of Reference

  • An example of an inertial reference system is a train station platform. The platform doesn't move, so it meets the criteria of not accelerating. Objects on the platform follow the law of inertia. 

  • A ball that rolls across the platform will continue to roll at a constant velocity until an external force is applied. The bench on the platform will not move without external force. This applies to the entire platform area.

  • Trains approaching the platform also follow the law of inertia. When the braking force is applied, it only slows down. Without this force, it will pass through the platform at a constant speed. 

  • An inertial coordinate system can indicate motion as long as its motion is at a constant velocity and maintains its direction of motion. An example of this is a car set for cruise control to drive on a straight road at a stable pace.

Non-Inertial Frame of Reference

  • The non-inertial frame of reference moves faster than the expected inertial frame of reference. Newton's law does not apply to such situations. However, to do this, you need to use a strange power called pseudo power.

  • By definition, an inertial frame of reference is a frame that is neither moving nor moving at a constant velocity. You can drive at a constant speed in a non-inertial coordinate system and accelerate at the same time, or you can drive at a constant speed on a circular path.

  • The non-inertial coordinate system is an accelerated coordinate system compared to the default inertial coordinate system. In general, accelerometers in such frames detect non-zero accelerometers when the frame is out of balance.

  • According to Newton's second law of motion, it is often possible to include additional apparent force (also known as inertial force or pseudo force) in an equation that describes the movement of an object. Coriolis and centrifugal forces are two reference examples of non-inertial frames.

  • There is no global inertial reference system in general relativity due to the non-Euclidean geometry of curved spacetime due to the curvature of spacetime. The imaginary force generated by the general theory of relativity is gravity, and more frankly.

Example of Non-Inertial Frame of Reference

  • Let's say, you are in the car at a traffic light. The car is stationary. The traffic light turns green and the car accelerates forward. During this acceleration, the car is in a non-inertial frame of reference.

  • A reference frame attached to the earth A Is an inertial frame by definition B Cannot be an inertial frame because the earth is revolving around the sun. C Is an inertial frame because Newton's laws are applicable in this frame D Cannot be an inertial frame because the earth is rotating about its own axis. 

  • The frame of reference that moves with a constant speed as well as the frame of reference which is neither rotating nor accelerating is known as the inertial frame of reference. Since the earth rotates about its coordinate axis and orbits the sun thus Earth is not an example of a non-inertial frame.

Difference Between Inertial and Non-Inertial Frame of Reference

Inertial Frame of Reference

Non-Inertial Frame of Reference

Moves at a constant velocity (can be zero).

Bodies move at variable speeds

Follows Newton's law.

Newton's law is not obeyed.

bodies do not accelerate.

The body experiences acceleration

The force acting on the body is the actual force.

Acceleration of frames creates a pseudo force

Example: A rocket in intergalactic space (a space without gravity between galaxies) with the engine turned off.

Example: If the car has just started moving from a standstill, the car is in the non-inertial coordinate system during acceleration.

Summary

A frame of reference is required to measure various quantities such as displacement, velocity, and acceleration. A reference frame is an abstract coordinate system whose direction, origin, and scale are specified by a set of geometric reference points whose positions are mathematically and physically identified. A reference frame connected to an object that is stationary or moving at a constant speed is called an inertial reference frame. In the inertial reference system, Newton's first law of motion is applied directly. A coordinate system to which Newton's first law of motion does not apply directly is called a non-inertial coordinate system. In this case, we use pseudo-forces to test Newton's first law.

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FAQs on Inertial and Non-Inertial Frame of Reference - JEE Important Topic

1. The earth as a frame of reference. Discuss.

The earth can be a non-inertial frame of reference. So far, we are aware of the fact that a frame of reference is a coordinate system that can be a frame of reference in which an object is moving at a continuous velocity or is stationary. In such a frame, the object is not accelerating, so there is no net force acting on it. However, in a non-inertial coordinate system, the movement of an object is affected by conceptual and other external forces. When the earth rotates, an external force is generated and the movement of the object accelerates. This means that the world is not an inertial frame of reference.

2. Explain the relative motion?

The concept of relative motion in one or more dimensions is based on the idea of reference frames. When an object has  given any velocity, then this velocity with respect to some frame is known as the reference frame. In daily life, the ground or the earth is assumed to be the reference frame when measuring an object's velocity.

For example, if you are travelling in a train that is moving at 100 km/hr, another passenger on the train will perceive your speed as zero. He claims that you aren't moving. However, if someone were to witness you while standing outside the train, he would claim that you were going at a speed of 100 km/h because you were inside the train and it was also moving at that speed.

In this case, the observer's location (or "frame") affects the motion that is visible. This motion is known as Relative motion.