# Pseudo force

let me first donate a(A,B) is the acceleration of A relative to B
Observer 2 and a subject A with mass m are falling down from a building
Observer 1 is standing on the ground to observe the motion of these two objects
Ignore the air resistance
In observer 1,he sees the force acting on A
=ma(A,1)
=m[a(A,2)+a(2,1)]
In observer 2,he sees the force acting on A
=ma(A,2)
Obviously a(A,2)=0,but this doesn't make sense
So, we introduce pseudo force f=-ma where a is the acceleration of the frame
The problem is here,which equation should I add the pseudo force into?
I don't know the above assumption is correct or not,please check!

## Answers and Replies

Doc Al
Mentor
The pseudo force is added when viewing things from the accelerated frame.

Andrew Mason
Science Advisor
Homework Helper
let me first donate a(A,B) is the acceleration of A relative to B
Observer 2 and a subject A with mass m are falling down from a building
Observer 1 is standing on the ground to observe the motion of these two objects
Ignore the air resistance
In observer 1,he sees the force acting on A
=ma(A,1)
=m[a(A,2)+a(2,1)]
In observer 2,he sees the force acting on A
=ma(A,2)
Obviously a(A,2)=0,but this doesn't make sense
So, we introduce pseudo force f=-ma where a is the acceleration of the frame
The problem is here,which equation should I add the pseudo force into?
I don't know the above assumption is correct or not,please check!
Why does a(A,2) = 0 or ma(A,2) not make sense? They are both falling at the same rate so their relative acceleration is 0. Both are in a state of free-fall and experiencing no inertial effects. As far as I can see, there is nothing that would require introduction of a pseudo force to explain.

AM

Doc Al
Mentor
Leaving general relativity aside, there is a gravitational force acting on the mass yet the acceleration is zero in the falling frame. Thus a pseudo force is introduced to rationalize Newton's laws.

Andrew Mason
Science Advisor
Homework Helper
Leaving general relativity aside, there is a gravitational force acting on the mass yet the acceleration is zero in the falling frame. Thus a pseudo force is introduced to rationalize Newton's laws.
But, unlike acceleration due to an electrical force, say, the accelerating observer observes no inertial effects that would require introduction of an inertial force.

The pseudo force that is required in the case of an electrical central force is a centrifugal force. The charged body that is subject to the electrical force experiences an inertial effect that is opposite to the direction of the electrical force. So a centrifugal pseudo force is introduced to explain that effect in the accelerating body's frame. But no such effect appears with a body that is subject only to a gravitational force. The reference frame of a body in gravitational freefall/orbit is equivalent to an inertial frame. If a pseudo force is introduced you would no longer have a frame of reference that is equivalent to an inertial frame.

AM

A.T.
Science Advisor
The reference frame of a body in gravitational freefall/orbit is equivalent to an inertial frame.
That's why gravity can modeled as a inertial force, and in General Relativity it is. But this is the classical physics forum, where gravity is an interaction force.
If a pseudo force is introduced you would no longer have a frame of reference that is equivalent to an inertial frame.
Sure you would. In the classical non-inertial free falling frame, the inertial force exactly cancels the force of gravity. So that frame is equivalent to an inertial frame with no gravity acting.

So, we introduce pseudo force f=-ma where a is the acceleration of the frame.

I wouldn't say that we introduce the pseudo force. It simply results from Newton's second law.

Andrew Mason
Science Advisor
Homework Helper
That's why gravity can modeled as a inertial force, and in General Relativity it is. But this is the classical physics forum, where gravity is an interaction force.

Sure you would. In the classical non-inertial free falling frame, the inertial force exactly cancels the force of gravity. So that frame is equivalent to an inertial frame with no gravity acting.
If I carry a net charge (one my shoes, say) and I am being whirled around a body by a central electrical force, I experience something that is trying to rip me out of my shoes. So, in my reference frame I postulate a centrifugal force acting on me trying to send me away from my shoes. The pseudo force allows me to analyse motion in my (non-inertial) reference frame.

But I don't have this effect with gravity as the only real force. Since I cannot sense gravity as a force there is no reason to introduce a force to counteract it. Unless one is experiencing tidal effects in free-fall, I have difficulty understanding why it would be necessary to introduce a pseudo force.

In this respect, there is a fundamental difference between gravity and other forces even in classical physics. I don't think you need GR to explain that difference.

AM

A.T.
Science Advisor
Since I cannot sense gravity as a force there is no reason to introduce a force to counteract it.
What you can sense is completely irrelevant. In classical mechanics the free falling frame (in a g-field) is an accelerated frame. In an accelerated frame there is an inertial force, per definition. Period.

In this respect, there is a fundamental difference between gravity and other forces even in classical physics.
Yes, it behaves like inertial forces. But in classical physics it is still modeled as a real force.

I don't think you need GR to explain that difference.
It is about how gravity is modeled:
Newton : real force
Einstein : pseudo force

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Andrew Mason
Science Advisor
Homework Helper
In an accelerated there is an inertial force, per definition. Period.
There is no inertial "force". Are you suggesting there is an inertial effect? How does it appear?

AM

A.T.
Science Advisor
In classical mechanics the free falling frame (in a g-field) is an accelerated frame. In an accelerated frame there is an inertial force, per definition.
There is no inertial "force".
http://en.wikipedia.org/wiki/Fictitious_force

Andrew Mason
Science Advisor
Homework Helper
Which is exactly my point. It is not a real "force". It is an inertial effect. But that is just terminology. My question is what inertial effect does a pseudo force explain if the only real force is gravity?

AM

A.T.
Science Advisor
There is no inertial "force".
Which is exactly my point. It is not a real "force".
No, that wasn't your point. You said that there is no inertial force, which is wrong.
My question is what inertial effect does a pseudo force explain if the only real force is gravity?
The lack of coordinate acceleration from that single real force acting.

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Andrew Mason
Science Advisor
Homework Helper
No, that wasn't your point. You said that there is no inertial force, which is wrong.
No. I said there is no inertial "force". My point in saying that, and my only point, was an inertial effect not a "force". It isn't.
The lack of coordinate acceleration from that single real force acting.
What do you mean? Can you give me an example of a phenomenon observed in the free-falling frame that requires introduction of a pseudo force to explain?

AM

Can you give me an example of a phenomenon observed in the free-falling frame that requires introduction of a pseudo force to explain?

The rest frame of ISS is a free-falling frame. As ISS is at rest there is no net force. But as there is a gravitational force acting between ISS and Earth there must be a pseudo force keeping ISS at its position.

Andrew Mason
Science Advisor
Homework Helper
The rest frame of ISS is a free-falling frame. As ISS is at rest there is no net force. But as there is a gravitational force acting between ISS and Earth there must be a pseudo force keeping ISS at its position.
?? Why? The ISS is accelerating. No pseudo force is needed to keep the ISS in its orbit.

In the rest frame of the earth, the motion of the ISS is completely explained by gravitational force.

In the rest frame of the ISS, there are no phenomena appearing that require a pseudo force to explain.

AM

Doc Al
Mentor
?? Why? The ISS is accelerating. No pseudo force is needed to keep the ISS in its orbit.
In the rest frame of the ISS there is no acceleration.

In the rest frame of the earth, the motion of the ISS is completely explained by gravitational force.
Right. And that gravitational force exists in all frames. In the rest frame of the earth, there is a gravitational force and the resulting acceleration; no modifications to Newton's laws are required.

In the rest frame of the ISS, there are no phenomena appearing that require a pseudo force to explain.
You have a gravitational force yet no acceleration.

A.T.
Science Advisor
I said there is no inertial "force".
There is an inertial force, because it is a accelerated frame.
Can you give me an example of a phenomenon observed in the free-falling frame that requires introduction of a pseudo force to explain?
Inertial forces are introduced to make Newton's 2nd law applicable to non-inertial frames, not to "explain phenomenons".

Andrew Mason
Science Advisor
Homework Helper
You have a gravitational force yet no acceleration.
So what pseudo force do you introduce?

[Comment: Pseudo forces are introduced in order to apply Newton's laws of motion when the accelerating reference frame is treated as an inertial reference frame.

One can apply Newton's laws in the accelerating reference frame, treating it as an inertial frame, without introducing any pseudo forces. You cannot do that if the frame is accelerating due to central mechanical or electric force. You can only do that with a non-inertial reference frame that is in gravitational free-fall.

So my question is: why do we have to introduce a pseudo force in this case?]

AM

Andrew Mason
Science Advisor
Homework Helper
Inertial forces are introduced to make Newton's 2nd law applicable to non-inertial frames, not to "explain phenomenons".
But Newton's laws of motion work perfectly in a non-inertial reference frame that is experiencing only gravitational force. You do not need a pseudo force to make them work. If you disagree, tell us what pseudo force is needed in order to make f=ma work in a reference frame that is in gravitational free-fall.

Am

A.T.
Science Advisor
what pseudo force is needed in order to make f=ma work in a reference frame that is in gravitational free-fall.
Did you read the wiki?
http://en.wikipedia.org/wiki/Fictitious_force
In a coordinate system K which moves by translation relative to an inertial system k, the motion of a mechanical system takes place as if the coordinate system were inertial, but on every point of mass m an additional "inertial force" acted: F = −m a, where a is the acceleration of the system K

Doc Al
Mentor
So what pseudo force do you introduce?
-ma, of course.

[Comment: Pseudo forces are introduced in order to apply Newton's laws of motion when the accelerating reference frame is treated as an inertial reference frame.

One can apply Newton's laws in the accelerating reference frame, treating it as an inertial frame, without introducing any pseudo forces. You cannot do that if the frame is accelerating due to central mechanical or electric force. You can only do that with a non-inertial reference frame that is in gravitational free-fall.

So my question is: why do we have to introduce a pseudo force in this case?]
Once again: If you do not introduce an inertial force, you will have an unbalanced force (gravity just doesn't disappear because you shifted frames) but no acceleration.

Apparently you chose to disregard the gravitational force when you changed frames. Again, this is not general relativity.

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Andrew Mason
Science Advisor
Homework Helper
-ma, of course.

Once again: If you do not introduce an inertial force, you will have an unbalanced force (gravity just doesn't disappear because you shifted frames) but no acceleration.

Apparently you chose to disregard the gravitational force when you changed frames. Again, this is not general relativity.
I didn't disregard the gravitational force any more than I disregard the central Coulomb force when I imagine a centrifugal force pulling me away from my charged shoes. In the electrical case I needed a pseudo force to explain why I fly off when my shoelaces break. In the gravitational case I don't. That's the difference.

So what is the inertial "force" that I postulate in the gravitational case. It cannot be the same force as in the electrical case.

AM

A.T.
Science Advisor
In the electrical case I needed a pseudo force to explain why I fly off when my shoelaces break.
In the free falling frame you need a pseudo force to explain why free falling objects do not fly down, due to gravity.
In the gravitational case I don't. That's the difference.
There is no difference. The concept of inertial forces is general and applies to all accelerated frames. It is completely irrelevant what types of real forces act.
So what is the inertial "force" that I postulate in the gravitational case.
Did you read the wiki?
http://en.wikipedia.org/wiki/Fictitious_force
In a coordinate system K which moves by translation relative to an inertial system k, the motion of a mechanical system takes place as if the coordinate system were inertial, but on every point of mass m an additional "inertial force" acted: F = −m a, where a is the acceleration of the system K

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Andrew Mason
Science Advisor
Homework Helper
In the free falling frame you need a pseudo force to explain why free falling objects do not fly down, due to gravity.
But they do fall down due to gravity.
There is no difference. The concept of inertial forces is general and applies to all accelerated frames. It is completely irrelevant what types of real forces act.
That is where we disagree. I say that pseudo forces do not arise if the acceleration of the frame of reference is due to gravity.
Did you read the wiki?
http://en.wikipedia.org/wiki/Fictitious_force
"In a coordinate system K which moves by translation relative to an inertial system k, the motion of a mechanical system takes place as if the coordinate system were inertial, but on every point of mass m an additional "inertial force" acted: F = −m a, where a is the acceleration of the system K"
And that is fine if the acceleration of K is due to any force except gravity.

The problem is that "the motion of a mechanical system" in gravitational free-fall "takes place as if the co-ordinate system were inertial" WITHOUT introducing an additional "inertial force" on every point mass m of F = -ma. In fact, it is locally equivalent to an inertial frame of reference (ignoring tidal forces).

If I introduce a force F=-ma on all objects in the frame of reference that is in gravitational free fall, there will be relative motion or tensions within that frame of reference. Where the acceleration of K is due to mechanical or electrical force, this is certainly the case. But not if the acceleration is due to gravity.

AM