# Pseudo forces are real forces?

• Ashu2912
In summary, pseudo forces are not considered "real" forces, but rather inertial forces that are treated as real forces in non-inertial frames to allow for the application of Newton's second law. They are necessary for accurately describing motion in non-inertial frames and can also be used to solve problems involving energy conservation. However, they do not obey Newton's third law and are therefore not considered true interaction forces.
Ashu2912
Pseudo forces are real forces?

Hey guys, I really need an insight into what exactly are pseudo forces? When I saw the derivation, it was more of a mathematical calculation, to find the acceleration of a particle with respect to a non inertial frame of reference. But doesn't the second law of motion strictly apply to inertial frames only, so why to extend it to non inertial frames just because the expression looks like the one in the second law? Is it meaningful to talk about forces, with the non inertial frame of reference? And if it is not even some force, and say we are applying the law of conservation of energy wrt some non-inertial frame, do we have to include it as an external force?

Ashu2912 said:
But doesn't the second law of motion strictly apply to inertial frames only, so why to extend it to non inertial frames just because the expression looks like the one in the second law?
It is often very convenient (or even necessary) to describe the motion from an accelerating frame. Introducing pseudo forces allows you to apply Newton's 2nd law.
Is it meaningful to talk about forces, with the non inertial frame of reference?
Why not? "Real" forces (interaction forces between objects, for instance) exist in all frames.

(To address the title of this thread: No, I would not call pseudo forces 'real' forces. They are just an artifact of viewing things from a noninertial frame.)

"Pseudo forces" vs. "real forces" is really a misleading naming convention, because it suggests that the "real forces" are somhow more "real", while they are also just an abstract concept and a mathematical tool. IMHO better names are:

pseudo forces = inertial forces
real forces = interaction forces

Ashu2912 said:
so why to extend it to non inertial frames just because the expression looks like the one in the second law?
Non-inertial frames are sometimes more practical to do math in.

Ashu2912 said:
And if it is not even some force, and say we are applying the law of conservation of energy wrt some non-inertial frame, do we have to include it as an external force?
Yes, the inertial forces fields introduce potential energy, which you have to account for to use energy conservation in non-inertial frames.

But you will not be able to use momentum conservation in the non-inertial frames, because inertial forces do not obey Newtons 3rd Law.

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I think the answer to your question depends on who you ask. A physicist will tell you that inertial forces are just a mathematical trick for being able to apply Newton's 2nd law to a non-inertial frame.

If you ask an engineer, he will tell you "hell yeah, of course they are real forces, just get into a fighter jet with 8 g's loopings, climbs and turns, come back to the ground and after throwing up, you'll understand why they are "real forces"

To add some practical-application perspective, we live on one big non-inertial frame (the spinning earth) that seems very inertial to our limited human senses. The introduction of pseudo forces to pretend a non-inertial frame is inertial is a very intuitive approach because of where we live. Perhaps if we lived on non-spinning, non-orbiting planet, the pseudo-forces approach would not seem so intuitive or so useful.

Why we use and introduce non inertial forces?

This is because we want to view the scenario from the point of view of a non-inertial observer and use Newtons law from his frame.
Using psuedo forces help us (both mathematically and physically) in describing the motion correctly.
The only reason the word psuedo is used is because the origin of force seems to be unknown from that frame whereas from the inertial frame the reason of origin of force can be identified.

For eg : Suppose ground is an inertial frame(we know it isn't but let's say we are performing this experiment on a different planet which doesn't rotate and is at rest)

let a man moving at 2m/s^2 wrt ground (he doesn't know he is moving at 2m/s^2.infact he thinks he is in an inertial frame ) observe a car moving at -2m/s^2 wrt him (i.e the car is at rest wrt ground.the ground also appears to slide below him with acceleration -2m/s^2).
he thinks some force is acting on the car but can't explain the name (or kind)of force
And the source which is applying this force.(that is why psuedo forces don't obey Newtons third law.As there is no identifiable source on which reaction acts)

To account for all this he makes an educated guess that he is not in an inertial frame himself and is moving with some acceleration and to account for this he adds a psuedo force on the free body of diagram of car.(nothing is known about who provides this force.its just an intelligent manipulation to account for observation.)

So psuedo is just used to reflect that the source of force is missing/unknown.

A person at rest wrt ground will observe the car at rest abd will know that no force is acting and so will have no such problem.

Now for answering your question if psuedo forces are real i would requore what A.T. said (as i feel he was spot on)
A.T. said:
"Pseudo forces" vs. "real forces" is really a misleading naming convention, because it suggests that the "real forces" are somhow more "real", while they are also just an abstract concept and a mathematical tool. IMHO better names are:

pseudo forces = inertial forces
real forces = interaction forces

For using work energy theorem (conservation of energy is a special case of work energy theorem )you will have to consider psuedo force as an external force and apply the theorem.

Although you cannot use conservation of momentum as external psuedo force acts(same reason why you can't apply conservation of energy but will have to apply work energy theorem), you can use Newtons second law (and also third for all other non-psuedo forces you observe like gravity) to account for new velocity's after collision.

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Ashu2912 said:
Pseudo forces are real forces?
Depends on the situation. For example imagine an accelerating rocket isolated in space, free of any external forces. If a person inside is holding a ball, then the person feels a pseudo force that corresponds to the inertial reaction of the ball to acceleration. The person is holding the ball, exerting an opposing force to the psuedo force, so there is zero net force on the ball in the accelerating frame, and the ball doesn't move within the accelerating frame. From an inertial frame of reference, the ball is accelerating and the net force on the ball is due to the person holding the ball, resulting in the ball accelerating, and exerting an equal and opposing reaction force onto the person's hands.

If the person inside drops the ball, then during the ball's "free fall", the person in the accelerating rocket observes what appears to be a pseudo force accelerating the ball "downwards", but from an inertial frame of reference, the ball is observed moving at constant velocity, with zero acceleration and zero real force.

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The most known fictitious/pseudo force called the Centrifugal force. It is fictitious since its acting alone, no action reaction. Real force obeys 3rd law, action reaction. We assume that there is a force that push us outside of the car when the car making a turn or speeding around a circular section. Same at centrifuge machine.

azizlwl said:
The most known fictitious/pseudo force called the Centrifugal force.

no, my vote is for good ol' gravity

it's certainly inertial (ie, proportional to mass),

and in general relativity, it's geometry, rather than a "real" force!

The main doubt I have here lies in the derivation, i guess :-
We have an inertial frame F, a non-inertial frame G, and a particle P, of mass m, which remains constant at all times
At any time,
Acceleration of G wrt F is $\stackrel{\rightarrow}{a}$G,F
Acceleration of P wrt G is $\stackrel{\rightarrow}{a}$P,G
Now,
m$\stackrel{\rightarrow}{a}$P,G = m$\stackrel{\rightarrow}{a}$P,F - m$\stackrel{\rightarrow}{a}$G,F [From relative acceleration concept)

Now, from Newton's Second Law applicable only to inertial reference frames,
$\stackrel{\rightarrow}{F}$P wrt F = m$\stackrel{\rightarrow}{a}$P,F.

Thus,
m$\stackrel{\rightarrow}{a}$P,G = $\stackrel{\rightarrow}{F}$P wrt F - m$\stackrel{\rightarrow}{a}$G,F

The problem I have is that in my book, m$\stackrel{\rightarrow}{a}$P,G is written as $\stackrel{\rightarrow}{F}$P wrt G, in a non inertial frame, whereas Newton's 2nd Law is valid only in inertial reference frames.

I am able to solve kinematics problems using the relation which I think is true, without even knowing what a pseudo force is, but i still don't get the idea of the pseudo force as an external force on the particle or system of particles.

Ashu2912 said:
The problem I have is that in my book, m$\stackrel{\rightarrow}{a}$P,G is written as $\stackrel{\rightarrow}{F}$P wrt G, in a non inertial frame, whereas Newton's 2nd Law is valid only in inertial reference frames.
If you account for inertial forces, then Newton's 2nd Law holds in non inertial frames too. That's the whole point of inertial forces.
Ashu2912 said:
but i still don't get the idea of the pseudo force as an external force on the particle or system of particles.
The idea is to make Newton's 2nd Law work in non inertial frames.

Hi Ashu2912!
Ashu2912 said:
Now,
m$\stackrel{\rightarrow}{a}$P,G = m$\stackrel{\rightarrow}{a}$P,F - m$\stackrel{\rightarrow}{a}$G,F [From relative acceleration concept)

But this only applies for frames with the same orientation.

In those frames, yes, the fictitious force is just another name for the relative acceleration (times mass) (even so, the concept of fictitious force is still helpful … for example, a horizontal "fictitious gravity" in an accelerating vehicle makes the angle of lean, or the motion of a pendulum, fairly obvious ).

Most non-inertial frames, however, are rotating

the concept of fictitious force (centripetal, coriolis, and euler) in those frames is very useful.

Ashu2912 said:
At any time,
Acceleration of G wrt F is $\stackrel{\rightarrow}{a}$G,F
Acceleration of P wrt G is $\stackrel{\rightarrow}{a}$P,G
Now,
m$\stackrel{\rightarrow}{a}$P,G = m$\stackrel{\rightarrow}{a}$P,F - m$\stackrel{\rightarrow}{a}$G,F [From relative acceleration concept)

This formula is valid only when the frames are non - rotating (As Tiny Tim pointed out) which is the case at high school level.
Just pointing it out so that you know, we are working on a v basic case here.

Now, from Newton's Second Law applicable only to inertial reference frames,
$\stackrel{\rightarrow}{F}$P wrt F = m$\stackrel{\rightarrow}{a}$P,F.

Thus,
m$\stackrel{\rightarrow}{a}$P,G = $\stackrel{\rightarrow}{F}$P wrt F - m$\stackrel{\rightarrow}{a}$G,F

See the basic point is that a person in frame G will measure acceleration as
$\stackrel{\rightarrow}{a}$G,F

If he has to use Newtons law in the form of F net = Ma,

He will have to say that the net force acting on particle is
M$\stackrel{\rightarrow}{a}$G,F

which is mass times the acceleration he measured and also the LHS of equation.

Now look at RHS.
It contains two terms.

One is the real force acting on particle $\stackrel{\rightarrow}{F}$P wrt F

m$\stackrel{\rightarrow}{a}$G,F

which has to be introduced to make the person be able to use Netwons 2nd Law (which is using Net force= Ma from his frame .Remember he calculated a wrt his frame)

This extra term is what is your fictious force.

We assosciate this extra term with force because it has dimensions of force.
Also a person in the accelerating frame will feel that some additional unknown forces (apart from the real ones) are acting on P

The source of these forces will be unknown so he will call them as fictitous forces.

-----
To be honest this is a vast topic with many important points and results.

http://www.scribd.com/doc/8789992/David-Morin-Introductory-Classical-Mechanics-with-Problems-and-Solutions-2004

And check out the article on fictious forces.

It has the derivation for the basic case and once you read it You will have no doubts remaining :-)

The basic idea is that we have to modify Newtons Laws so that we can use them in non intertial frames( which is what A.T. said )

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## 1. What are pseudo forces?

Pseudo forces, also known as fictitious forces, are forces that appear to act on a body but are actually due to the frame of reference in which the body is observed.

## 2. How do pseudo forces affect motion?

Pseudo forces can affect the motion of a body by causing it to accelerate or change direction in a non-inertial frame of reference. This is because they are not due to any physical interaction, but rather the observer's perspective.

## 3. Are pseudo forces considered real forces?

Yes, pseudo forces are considered real forces because they have a measurable effect on the motion of a body. They may not be caused by a physical interaction, but they are still valid forces within a non-inertial frame of reference.

## 4. What is an example of a pseudo force?

A common example of a pseudo force is the centrifugal force. When an object is rotating in a circular motion, it appears to experience an outward force, but in reality, this force is due to the frame of reference of the rotating object.

## 5. How do we account for pseudo forces in calculations?

In order to accurately calculate the motion of a body in a non-inertial frame of reference, we must include the effects of pseudo forces in our calculations. This can be done by using mathematical equations and principles that account for the frame of reference and the resulting forces.

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