Question

Which of the three laws of motion by newton hold in non-inertial(accelerating) reference frames?

Answer 1

@Loser66

Answer 2

second law F = ma

Answer 3

Are you sure. because in Professor walter lewins' lecture 6 of 8.01 He says that the second law does not hold in non inertial frames of reference.
Here's the link:
http://ocw.mit.edu/courses/physics/8-01-physics-i-classical-mechanics-fall-1999/video-lectures/lecture-6/

Answer 4

@MayanD
It depends on how you apply (or define) the law.

As you would be aware, we use the concept of pseudo force to apply newton's law in a non inertial reference frame.

Now try to analyze the situation without acknowledging the presence of pseudo force.

1st law: It would be violated as a body may change both the direction and magnitude of its velocity without the detection of any force (which we can relate to its environment).

2nd law: It would be violated in the sense that the summation of force vectors and acceleration vectors won't obey F=ma

However, the individual forces and their corresponding accelerations will follow the 2nd law (although it will be hard to determine experimentally).

3rd law: As pseudo force cannot be attributed to any other object in the environment of the concerned object, it will not have a action-reaction conjugate.

Again, all other forces will still follow the 3rd law (and again it will be hard to determine experimentally)

Answer 5

Exactly what i was looking for. But do we take these pseudo forces into consideration while using these laws or not

Answer 6

@MayankD
If you can leave the question open for sometime, I would like to ask a follow-up question from the community.

Answer 7

Sure

Answer 8

The problem with non-inertial frames is that there exists an acceleration vector without the corresponding force vector.

So, we introduce a force vector (namely pseudo force) to be able to use 1st and 2nd law of motion in our analysis. Still the third law remains violated.

Answer 9

@Physics_Community

Can someone explain the difference between inertial and non-inertial reference frames? Or define them?

Answer 10

If we acknowledge the use of pseudo force then the third law is valid too right?

Answer 11

No, there is no action-reaction pair for a pseudo force or in other words, it is singular.

Answer 12

Ok fair enough

Answer 13

@ganeshie8 @nubeer @oksuz_

Can someone explain the difference between inertial and non-inertial reference frames? Or define them?

Answer 14

Only the third law remains valid.
The fist ans second laws do not hold. As we still want of use them, without going back to an inertial frame, we have invented the concept of inertial forces. They are mathematical artefacts that deal with the non-inertial character of the frame.

Answer 15

@Vincent-Lyon.Fr
Please explain how is 3rd law of motion valid in non-inertial reference frame?

Answer 16

Whatever the frame, if A exerts a force on B, then B exerts the opposite force on A.

Answer 17

But a pseudo force cannot be attributed to any other object in the environment of the 1st object. So how can you find the action-reaction pair for pseudo force?

Answer 18

Oh ok i get it. The pseudo force does not exist . it is just a mathematical expression to make the first two laws work. Ergo it is not a real force so it wont affect the third law which is for real forces

Answer 19

But a pseudo force is not a force (only a mathematical artefact).
Newton's third law only deals with real interactions.

Answer 20

Thanks i get it now!

Answer 21

MayankD , you are 100% right ! :-)

Answer 22

@Vincent-Lyon.Fr
Can you explain the difference between inertial and non-inertial reference frames? Or define them?

Answer 23

^^ What I mean to ask is - how to determine whether a given frame of reference is inertial or non-inertial??

Answer 24

The problem is that it is a circular definition:
"A frame is inertial if all three N's laws are valid."

So only experiment will tell you if a frame is inertial or not.

Earth reference frame is inertial up to a certain accuracy of your measures. In most experiments, it is, but such devices as Foucault's pendulum of deviation in free fall prove that the earth is a rotating frame.

Geocentrical frame and heliocentrical frames are inertial to a better degree.

Answer 25

Do inertial reference frames actually exist or are they just theories (like "ether") waiting for experimental scrutiny?

In other words, does acceleration of a body has an absolute value or is it relative (analogous to velocity)?

Answer 26

We cannot prove with certainty whether a frame is inertial or not. As to whether acceleration is relative or absolute , i have the same doubt. @Vincent-Lyon.Fr Can you answer that please?

Answer 27

In classical mechanics, you can say that acceleration is absolute and velocity is not. Although I do not like this statement.

In other words : you cannot prove that you are moving with respect to an inertial frame, whereas you can prove that you are accelerating.

As to whether inertial frames exist of not, Einstein showed that gravitational fields are equivalent to accelerating, so the question becomes irrelevant.

There is no "absolute" in physics (can you define the absolute length of your ruler?).
The frame linked to the centre of mass of the solar system (called Copernicus' reference frame in certain countries) is considered as quasi-inertial in all situatins.
http://en.wikipedia.org/wiki/International_Celestial_Reference_Frame