# Question related to inertia and non inertial frame

• parshyaa
In summary, when a person is standing on a bus that is moving with constant velocity and the driver suddenly applies the brakes, the person will move forward as if something pushed them from behind. This is due to the bus becoming a non-inertial frame and Newton's first law no longer applying. In order to make Newton's law workable in this frame, we must add a pseudo force. The person will continue moving at constant velocity until they hit something, at which point significant forces will be exerted on them. However, this situation is nonsensical and in reality, the person's movement would depend on various factors such as friction and stability. In a non-inertial frame where the net force on a body is zero,
parshyaa
Suppose a person is standing in a bus, moving with constant velocity and then driver applied the breaks and the person standing moved forward as if something pushed him from behind
Whats the reason behind this
Is it because bus has become a non inertial frame and we have to add psuedo forces to make it inertial frame

Or is it due to inertia(i.e its his body's ability to stay in motion even if the breaks are applied

https://en.wikipedia.org/wiki/Newton%27s_laws_of_motion said:
First law: In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.[2][3]

The person is one object. The bus is a different object. The objects can exert forces on each other.

anorlunda said:
The person is one object. The bus is a different object. The objects can exert forces on each other.
After applying breaks, bus is converted into a non inertial frame and in non inertial frame Newtons first law doesn't works, until we add psuedo forces. So we have to assume that there is a force(psuedo) which made hime to come forward. Whats wrong in this

Unless or until the bus or the air on the bus is exerting forces on the person, then they don't even come into the analysis. The person simply continues moving at constant velocity. Who cares what the bus is doing?

Last edited:
anorlunda said:
Unless or until the bus or the air on the bus is exerting forces on the person, then they don't even come into the analysis. The person simply continues moving at constant velocity. Who cares what the bus is doing?
Do you really think that air drag can push him so hard in bus moving with a decent speed, assume their is no air, then also we move forward when breaks are applied

I think like Newton's First Law. If there are no significant forces on the person, he continues moving at constant velocity. Doesn't matter if he's on a bus or in space.

Of course he'll eventually hit the front of the bus, and then there will be significant forces. But before that, it is as I said in the previous paragraph.

anorlunda said:
I think like Newton's First Law. If there are no significant forces on the person, he continues moving at constant velocity. Doesn't matter if he's on a bus or in space.

Of course he'll eventually hit the front of the bus, and then there will be significant forces. But before that, it is as I said in the previous paragraph.
Newton's first law fails in accelarting frames w.r.t bus, ie why we have to add psuedo forces to make Newton's law workable in that frame
We have to care what bus is doing(if its accelarting then its no longer a inertial fram and u can't say that accelaration is zero if and only if force is zero)

parshyaa said:
Newton's first law fails in accelarting frames w.r.t bus, ie why we have to add psuedo forces to make Newton's law workable in that frame
We have to care what bus is doing(if its accelarting then its no longer a inertial fram and u can't say that accelaration is zero if and only if force is zero)
We only have to care what the bus is doing if we are using the bus' non-inertial frame as our reference frame. We are under no obligation to do so, and many people would use the ground's frame instead.

Dale said:
We only have to care what the bus is doing if we are using the bus' non-inertial frame as our reference frame. We are under no obligation to do so, and many people would use the ground's frame instead.
So if i take bus as a reference frame then what is the cause for the accelartion of the body after applying the breaks and also the same with Earth as a reference frame.

If floor of bus was a frictionless surface then the body would continue in motion in same direction and at same velocity relative to the ground as before the brakes were applied . Until as @anorlunda says it hits something .

If floor was not frictionless then depending on the degree of friction force which was active the body may be wholly or partly constrained to move at the changing velocity of the bus relative to the ground as it slows down .

In reality this situation is nonsensical and what actually happens would depend on many detail and some chance factors . Not least of which would be the stability of the body .

Last edited:
Nidum said:
If floor of bus was a frictionless surface then the body would continue in motion in same direction and at same velocity relative to the ground as before the brakes applied . Until as @anorlunda says it hits something .

If floor was not frictionless then depending on the degree of friction force which was active the body may in addition be wholly or partly constrained to move at the changing velocity of the bus as it slows down .

In reality this situation is nonsensical and what actually happens would depend on many detail and some chance factors . Not least of which would be the stability of the body . It would probably just fall over .
Can you give me a example of a non inertial frame where net force on a body is zero and acceleration is non-zero or vice versa
What if the person is on rollers inside the bus, because similar example is given in university physics by sears and zemansky

See the highlighted part

#### Attachments

• IMG_20171014_231920482.jpg
38.6 KB · Views: 495
Last edited:
parshyaa said:
if i take bus as a reference frame then what is the cause for the accelartion of the body after applying the breaks
There is a fictitious force in that frame that accelerates the body.

parshyaa said:
and also the same with Earth as a reference frame
The body does not accelerate in that frame. It continues at the same speed (neglect any friction)

Dale said:
There is a fictitious force in that frame that accelerates the body.

The body does not accelerate in that frame. It continues at the same speed (neglect any friction)
So for Earth as a frame answer is simply inertia but when we take frame as bus then it will be a non-inertial frame and fictitious force will act on the body from behind
because acc. Is towards him
Is it correct

parshyaa said:
when we take frame as bus then it will be a non-inertial frame and fictitious force will act on the body
Yes.

parshyaa
Dale said:
Yes.
What is wrong in my statement related to earth, what would be the reason for his acceleration, if we watch him from Earth's reference frame

parshyaa said:
What is wrong in my statement related to earth, what would be the reason for his acceleration, if we watch him from Earth's reference frame
He is not accelerating in the Earth's reference frame.

parshyaa
Dale said:
He is not accelerating in the Earth's reference frame.
So from Earth's frame of reference he is moving with constant velocity even if the bus retarded or stoped, how could this possible, if bus is retarding from Earth's frame then person standing in it is also retarding?

parshyaa said:
So for Earth as a frame answer is simply inertia but when we take frame as bus then it will be a non-inertial frame and fictitious force will act on the body from behind
because acc. Is towards him
Yes, that seems accurate.

If one uses the earth-based reference frame, there is no change in motion. The passenger started in motion and remains in motion until the windshield on the bus hits him in the face. Or until he regains his balance and uses friction with the floor to match his deceleration to that of the bus. If he does regain his balance, his mass (which is the measure of his inertia) determines how much force from the floor is required to match accelerations this way.

If one uses the bus-based reference frame, there is a fictitious force associated with the acceleration of the reference frame. This force accelerates the man until he hits the windshield of the bus with his face. Or until he regains his balance and uses friction with the floor to compensate for the new fictitious force. If he does regain his balance, his mass (which is a measure of his inertia) determines how large the fictitious force is and, accordingly, how much force from the floor is required to match it.

Regardless of which frame is used to perform the analysis, the relative velocity of face and windshield or the force from floor on feet will be the same. You are free to use whichever one is easier to calculate with.

parshyaa
jbriggs444 said:
Yes, that seems accurate.

If one uses the earth-based reference frame, there is no change in motion. The passenger started in motion and remains in motion until the windshield on the bus hits him in the face. Or until he regains his balance and uses friction with the floor to match his deceleration to that of the bus. If he does regain his balance, his mass (which is the measure of his inertia) determines how much force from the floor is required to match accelerations this way.

If one uses the bus-based reference frame, there is a fictitious force associated with the acceleration of the reference frame. This force accelerates the man until he hits the windshield of the bus with his face. Or until he regains his balance and uses friction with the floor to compensate for the new fictitious force. If he does regain his balance, his mass (which is a measure of his inertia) determines how large the fictitious force is and, accordingly, how much force from the floor is required to match it.

Regardless of which frame is used to perform the analysis, the relative velocity of face and windshield or the force from floor on feet will be the same. You are free to use whichever one is easier to calculate with.
Thanks @jbriggs444 , this made it clearer and also @Dale

parshyaa said:
So from Earth's frame of reference he is moving with constant velocity even if the bus retarded or stoped, how could this possible, if bus is retarding from Earth's frame then person standing in it is also retarding?

You're confusing yourself with contradictory statements. Either 1) The person continues with constant velocity and eventually hits the front wall of the bus, or 2) The person's feet remain fixed on the same place on the bus floor (or he is belted to a seat), and therefore he accelerates/decelerates as part of the bus system. But you can't have both (1) and (2) at the same time.

anorlunda said:
You're confusing yourself with contradictory statements. Either 1) The person continues with constant velocity and eventually hits the front wall of the bus, or 2) The person's feet remain fixed on the same place on the bus floor (or he is belted to a seat), and therefore he accelerates/decelerates as part of the bus system. But you can't have both (1) and (2) at the same time.
Yes i just posted it in hurry, but i got the answer, i was right from bus reference its fictitious force and from Earth's frame its inertia

parshyaa said:
So from Earth's frame of reference he is moving with constant velocity even if the bus retarded or stoped, how could this possible, if bus is retarding from Earth's frame then person standing in it is also retarding?
I was assuming that friction was negligible. You didn't clearly specify what you wanted to consider, so I was assuming negligible friction and explicitly stated that assumption above.

For controlled braking friction is probably not negligible, but in a collision or emergency braking it probably is.

Does adding of forces in non inertial frame makes force as frame dependent or it is frame independent because psuedo forces are not real

In short
Is force frame dependent?

parshyaa

## 1. What is the difference between inertia and non-inertial frames?

Inertia refers to an object's tendency to resist changes in its state of motion, while non-inertial frames are frames of reference that are accelerating or rotating. In a non-inertial frame, objects may appear to experience fictitious forces due to the frame's acceleration or rotation.

## 2. How does inertia affect objects in a non-inertial frame?

In a non-inertial frame, objects may appear to experience fictitious forces due to the frame's acceleration or rotation. However, the objects themselves still possess their inertia and will resist changes in their state of motion.

## 3. Can objects in a non-inertial frame experience actual forces?

Yes, objects in a non-inertial frame can experience actual forces in addition to the fictitious forces caused by the frame's acceleration or rotation. These actual forces can be caused by interactions with other objects or external forces.

## 4. How does the concept of inertia relate to Newton's first law of motion?

Newton's first law of motion states that an object will remain at rest or in uniform motion in a straight line unless acted upon by an external force. This is directly related to the concept of inertia, as an object's inertia causes it to resist changes in its state of motion.

## 5. Can non-inertial frames be used to accurately describe the motion of objects?

Non-inertial frames can be used to accurately describe the motion of objects within the frame, as long as the fictitious forces caused by the frame's acceleration or rotation are taken into account. However, inertial frames are typically preferred for accurately describing the motion of objects in most situations.

• Mechanics
Replies
2
Views
885
• Mechanics
Replies
18
Views
1K
• Mechanics
Replies
6
Views
1K
• Mechanics
Replies
5
Views
1K
• Mechanics
Replies
25
Views
2K
• Mechanics
Replies
8
Views
933
• Mechanics
Replies
1
Views
850
• Mechanics
Replies
12
Views
2K
• Mechanics
Replies
17
Views
3K
• Mechanics
Replies
3
Views
1K