Understanding the Concept of Pseudo Force : Section I : Dealing with Frames of Reference

DEALING WITH FRAMES OF REFERENCE

Newton's laws are not valid in non-inertial frames. However, by using the concept of pseudo forces, we can freely apply newton's laws even in non-inertial frames. Pseudo forces are not real forces. We only use pseudo concept when we deal with objects which are in non-inertial frames.  

What the heck is this inertial or non-inertial frame ??

Okay, Before explaining the pseudo concept, I am going to shed some light on what inertial or non-inertial frames are.

FIRST LET'S SEE WHAT FRAMES ARE ?

 Consider a trolley moving with acceleration a1 with respect to ground. And again, the ball, which is inside the trolley, accelerates with acceleration a with respect to trolley. Now, If you ask the person sitting inside the trolley, he will say that the ball is accelerating with acceleration a. Again, if you ask a person who is sitting on a ground and watching the trolley moving, he will say that the ball is accelerating with acceleration a1+a. 

Now I want to ask you who says wrong ?

The answer to this is nobody says wrong. Although both persons A and B have different views on the acceleration of ball, yet both are correct in their own way. The difference in the views of persons A and B is only because the person B [on the ground] considers also the acceleration of trolley. whereas the person A [on the trolley] does not consider the acceleration of trolley.

We say that both persons A and B are standing on different frames. Now, we can define frames :
In simple language, a frame is a viewpoint for an object under-study i.e. the place from which the object is seen. In the above diagram, the person A is viewing the object from the trolley. So, trolley is the frame from which the ball is seen. Also, person B views the ball from ground. So, ground is the frame from which the ball is seen. Also note that the acceleration is different for "trolley-frame" and for "ground-frame". 

Getting a Little deeper into frames : Moving frames
Frames, from which we view an object, may be moving or may not be moving. Consider the example given above, the ground frame is a non-moving frame, it is stationary. But look, the trolley frame is a moving frame as it accelerates with acceleration a1. 

 Frames can be moving or non-moving. The frames which do not move (i.e. are at rest) or else are moving with constant velocity (i.e. with no acceleration) are called as inertial frames. And the frames which have acceleration are called as non-inertial frames. Newton's laws are not valid in non-inertial frames. In order to use newton's laws in non-inertial frames, we have to apply pseudo force (which is introduced later in this section.) 


Exercise : Can you identify these as inertial or non-inertial frames ??

1. An aeroplane which is accelerating in open air.
2. A Stone kept on a boat moving with constant velocity.
3. A block which is coming down with constant velocity down a ramp.
4. A bird increasing its speed to catch an earthworm on ground.
5. Our Earth

Solutions : 

1. The aeroplane is moving with acceleration. And hence, it is non-inertial frame.
2. The boat is moving with constant velocity. The stone which is kept on it is at rest on the boat. And so it moves with a velocity equal to that of boat. Note that the stone is moving but with constant velocity and no acceleration. Hence, the stone is an inertial frame. 
3. Since the block has a constant velocity, it is an inertial frame. 
4. The bird is increasing its speed i.e. it has acceleration [if speed of a body changes, that means it has acceleration]. Hence, it is a non-inertial frame.
5. The Earth rotates on its axis, and revolves around sun. It does not move with "precisely" constant velocity but has acceleration also. However, considering its acceleration, it has very small magnitude. And hence, for convenience, Earth is considered as an inertial frame.  

Rotating Frames ???

Come to think of it, Frames can also rotate with respect to a particular axis. Imagine you take a cricket ball, tie it to a rope and whirl it around you by catching at one end. The ball then will be a frame which is not only accelerated but also rotating with a particular acceleration and velocity. Such frames are also non-inertial frames. As I've told you above, all frames which move with acceleration are non-inertial, the same applies to rotating frames also. Note that you cannot directly apply newton's laws in rotating frames as these frames are non-inertial. Hence, you have to include a pseudo force to apply newton's laws for these rotating frames. Problems regarding Rotating frames are dealt with later in this section. 

Complex Frames :
Cases can arise when dealing with frames will become more and more difficult. You may also come across problems where a frame not only translates but also rotates with an acceleration. In such case you have to apply two pseudo forces, one to balance the rotational motion of frame and the other to balance the translational motion of frame. 

    Scope of "Understanding Frames"
Understanding the concept of Inertial and non-inertial frames are of great importance in physics. If one wants to have a clear understanding of classical mechanics, modern physics and most importantly relativity theory, he must have a clear understanding of the concept of frames. In order to proceed in this section for understanding the concept of pseudo forces, an understanding of frames is required.