Inertial frame of reference Class 11

By definition, we know that the frame of reference is defined as any coordinate system concerning which one can study the motion of another object. For example, a moving car can be a frame of reference to which anyone can learn the motion of another moving car by being in the first moving car itself. The most simple frame of reference is the Cartesian coordinate system. The position of a moving particle  at any instant is expressed in terms of coordinate ( x,y,z) or by position vector r = xi+yj+zk with origin O ( 0,0,0). 

As Albert Einstein said, knowledge is less necessary than imagination. Because knowledge is restricted, whereas imagination covers the entire world, promoting growth and allowing evolution to happen. And to understand this topic better, you need your vision because when you relate real-world examples, it is easier to understand and lasts forever. Let’s go deep and understand the basic concept behind the topic, like Velocity, and Relative Motion.

Velocity

Speed is a scalar quantity with only the magnitude, whereas Velocity is a vector quantity with both magnitude and direction. In other words, Velocity is the rate at which an object moves in a specific direction. The displacement of an object in a certain amount of time is referred to as Velocity, and velocity units include miles per hour, kilometers per hour, and meters per second. L T-1 represents the velocity dimension. Average Velocity is defined as the change in location divided by the journey time.

Velocity is represented by v = d / t

here, v = velocity

t = time taken by the object 

d = distance

What is the significance of velocity?

Velocity is a unit of measurement for the speed with which an object moves from one location to another in a particular direction. You use velocity measurements to determine how quickly you or any moving item will arrive at a destination from a particular starting point.

You may use velocity measurements to construct trip timetables and manage your schedule accordingly. For example, if a train departs ABC Station in Bangalore at 6 p.m. and you know the train’s velocity at the other station, you may estimate when the train would arrive at the destination station.

Relative

Relative motion is simply a way of explaining that different people will sometimes state different things about the motion of the same object. This is not because one is incorrect, but because they have different frames of reference. The simplest way to grasp this is to look at some examples. In all of the following cases, disregard air resistance.

Frame of Reference

 Let us consider the case to understand better; let’s say a car is moving at a speed of 100 km/hr now. While calculating the car’s speed, we completely ignore that the Earth’s surface is rotating at the equator with the speed of 1670 km/hr, and the velocity of the earth’s orbit around the sun is 30 km/s. So if we calculate the motion of the car, we can see the car is moving at tremendous speed because all the motion of earth and sun will be added to it now here comes the frame of reference into the picture.

let’s understand this mathematically : 

Case 1 – Now, if we take the frame of reference inside the earth, then the earth seems to be stationary; hence the speed of the car is 100 km/hr.

Case 2 – Now, if we take our frame of reference from outside the earth, say from the moon then we would see the car is moving with a speed of ( 100+1670 = 1770 km/hr) where the speed of the car and the rotating speed of the earth gets added. 

Case 3 – Now, if we take our frame of reference concerning the sun, we will get the speed of the car as 100+1670+108000 = 109770 km/hr, adding the speed of the car, the rotational speed of the earth, and the orbital speed of the earth around the sun.

Now, the car is moving at a considerable speed, but the car doesn’t appear to be at high speed. It only seems at 100 km/hr because of the frame of reference. Since the observer is in the frame of reference inside the earth and for the observer, the earth is stable. That is why the frame of reference comes into play. 

Types of Frames of Reference: 

1. Inertial Frame of Reference
2. Non-inertial Frame of Reference

Inertial Frame of Reference

For an inertial frame of reference, Newton’s law holds valid. This means that if no external (outer) force is acting on a body, it will remain at rest or in the same (uniform) motion. Assume an object is held on the earth’s surface; it is at rest for someone looking at it from the earth, while it is in motion for someone looking at it from the moon; which is my inertial frame in this case? The inertial frame of reference is relative because we regard a reference frame as the inertial frame of reference first. An inertial frame could be defined in a broader sense as, concerning the predicted inertial reference frame, the inertial frame is either stationary or moves at a constant velocity.

Non- Inertial frame of reference

Let us now define a non-inertial frame as accelerated in relation to the assumed inertial frame of reference. Newton’s law will not apply to these frames. So, in the preceding example, if I consider the earth an inertial reference frame and the moon a non-inertial reference frame, this is an accelerated motion concerning the earth. If we want to make Newton’s law, we must first establish a pseudo force.

Conclusion: 

One of the main theories of kinematics is the frame of reference. Kinematics provides information on the nature of the body’s movement in a specific situation based on a frame of reference. This frame of reference is also used to study relative motion between two bodies. In contrast to the inertial frame, a non-inertial frame of reference requires artificial forces to explain observations. Overall, the frame of reference is merely the beginning of a vast pool of intriguing topics such as mechanics, which is crucial for JEE.

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