All Questions
Tagged with galilean-relativity newtonian-mechanics
138 questions
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Is the definition of inertial reference frame circular?
In elementary physics classes, inertial reference frames are defined as a coordinate system which is in constant rectilinear motion (or at least that is how it was defined by my professor). How then ...
- 29
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vote
1
answer
90
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Could we deduce energy, momentum and angular momentum conservation laws from only Galilean relativity?
In Newtonian physics we could deduce conservation of energy, momentum and angular momentum from Newton's three laws.
But by Noether's theorem, conservation laws could be deduced from symmetries.
Could ...
- 1,419
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1
answer
50
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Invariance of Acceleration vs Invariance of Magnitude of Acceleration and help with proof
This question is a half-rant, half-question, as I am genuinely curious as to what the standard physics view is on this question. As someone who has studied math extensively (but not physics), please ...
2
votes
5
answers
195
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Violation of Newton's second law if the mass if changing?
I learned some thing called Galilean principle of relativity which says that two inertial frames are equivalent and the laws of physics are the same in both inertial frames.
However here comes the ...
- 421
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0
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58
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Independence of Lagrange function from time and position
In Landau & Lifshitz "Mechanics", it is said that from the time/space homogeneity Lagrange function is independent from time/position. I always thought that homogeneity means that motion ...
- 39
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3
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858
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What is the exact meaning of Galileo's principle of relativity?
Galileo's principle of relativity states that the laws of mechanics are invariant in every inertial frame of reference.
This is well illustrated by Galileo’s ship. What is meant here by "laws of ...
- 61
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2
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78
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Why is force independent of frame of reference (inertial)
This question has been bugging me for quite some time, I have seen some explanations which are mathematical and don't make sense to me, most of them talk about Galilean relativity, but I am looking ...
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1
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125
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How Feynman proves momentum is conserved in this example?
Here is what Feynman says in section I.10-3:
"Suppose we have two equal masses, one moving with velocity $v$ and the other standing still, and they collide and stick; what is going to happen? ...
- 121
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1
answer
247
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Action of free particle is invariant under Galilean transformation / Transformation of derivative
I want to show that the action of a free particle is invariant under a Galilean transformation
$$
(t,\vec{x})\rightarrow (t+a,R\vec{x}+\vec{v}t+b)=(t^\prime, \vec{x}^\prime) \quad\text{where}\quad R\...
- 405
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4
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277
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Why is it "forbidden" to use EM waves as a way of detecting motion in two different inertial frames?
Constant motion can not be detected by neither particles (because of inertia) nor mechanical waves ( because they need a medium ). However when you consider light for example and assume it does not ...
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4
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233
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Reference frame doubts about isotropy
Landau & Lifshitz on p.5 in their "Mechanics" book states the following:
...a frame of reference can always be chosen in which space is
homogeneous and isotropic and time is homogeneous....
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0
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137
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Why does the ball in Galileo's double inclined plane experiment reach the same height?
Why does the ball in Galileo's double inclined plane experiment reach the same height? I know how to show it by energy conservation law but am unable to prove it by the equations of motion. Can anyone ...
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77
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Principle of Relativity and the invariance of Newton's law in IRFs
Newton's law are form invariant under the coordinate substitutions:
$$
\tilde{x^{i}}=x^{i}+a^{i}
$$
This means that Newtons' equation of motion,
$$
F^{i}=m \frac{d^{2} x^{i}}{d t^{2}}
$$
(where $i=1,2,...
- 11
1
vote
1
answer
42
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Coordinate Transformation using a Matrix
Consider two inertial and resting frames $K$ and $G$. The only difference between the two frames is that the axes of $G$ has been rotated with $\theta$ with respect to $K$. $G$ is not constantly ...
- 193
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1
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93
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Galilean relativity in terms of homogenity for car example
I have a question related to Landau & Lifshitz's book. In that, he says:
If we were to choose an arbitrary frame of reference, space would be
inhomogeneous and anisotropic. This means that, even ...
- 535
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32
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How can I solve this problem about energy conservation according to different frames of reference?
We have two frames of reference: the Earth (E) and a train (T) uniformely moving at velocity u relative to the Earth.
We also have a particle that is initially stationary relative to the train, and is ...
- 435
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1
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83
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Inertial coordinate systems being invariant under time translation in Newton's Principle of Detrimancy
I have the same question posted as Newton's equation under time translation except I am not seeking the physical justification of the first claim but rather the mathematical justification of the ...
- 27
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66
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Center of Mass and Systems of Particles in Galilean relativity
Consider a reference frame in which two particles move with constant velocities $\vec{v}_1 = v_1 \hat{i}$ and $\vec{v}_2 = -v_2 \hat{i}$. Their center of mass would be the vector $\vec{R} = \frac{(...
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216
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What is metric (invariant) in Newton mechanics (equivalent to spacetime interval of Minkowski space)?
The answer might be obvious for those with much experience, but I could not get it via web search.
https://en.wikipedia.org/wiki/Minkowski_space
From the second postulate of special relativity, ...
- 151
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27
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Extending the Galilean transformation to the case of a possibly spacetime-dependent velocity field?
In all literature I have searched, the Galilean transform between two coordinates $(\overrightarrow{x},t)$ and $(\overrightarrow{x'},t')$ have been considered for a "constant velocity".
That ...
- 1,708
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2
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79
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In galilean relativity, is an observer assumed to be at rest only to simplify calculations, or is there a physical reason for this assumption?
I am a beginner in Physics and my teacher taught us "Relative Motion" yesterday. He said that the "Observer is assumed at rest." Is the observer assumed to be at rest only to ...
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1
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86
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Velocity addition as a special case of change of reference frame
In this question, I want to restrict the discussion to classical mechanics as understood before 1900; that is, to exclude any discussion of relativity (however, if there is a neat generalization I ...
- 1,261
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4
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692
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"Deriving" Newton's laws of motion from symmetry assumptions
It is often discussed how certain symmetries and conservation laws can be derived from Newton's laws of motion. My question is: can we go the other way? Can Newton's laws of motion be derived only ...
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205
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Forces that are invariant under Galilean spacetime rescaling $\mathbf x' = \lambda \mathbf x$, $t' = \lambda^2 t$
Consider a force of the form
$$
m \ddot{\mathbf x}(t) = -k\frac{\mathbf x(t) - \mathbf x_0}{|\mathbf x(t) - \mathbf x_0|^d}.
$$
For what values of $d$ is this force invariant under the Galilean ...
- 553
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4
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2k
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Doesn't Newton's equation of motion have a bigger invariance group than the Galilean group?
Newton's equation ${F}^i=m\frac{d^2x^i}{dt^2}$ is unchanged in form, under the Galilean group:
(i) under a translation of the origin of coordinates,
(ii) rotation of coordinates, and
(iii) Galilean ...
- 12.3k
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1
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61
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Is Newton's laws formulated using laboratory time?
The second Newton's law can be written as (in SI units)
$$
\frac{d}{dt}\vec p = \vec F.
$$
Newton was considered Galilean transformations and the existence of a "absolute" time. Now suppose ...
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3
answers
80
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Einsteinian principle of relativity in the limit of infinite propagation velocity
We can transform between inertial frames of reference using either the Lorentz transform in special relativity or the Galilean transform in the classical limit.
The Galilean transform gives: $$ x' = x ...
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298
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Is there any proof of Galilean Transformation?
Is there any proof of Galilean Transformation? Is it proved from experiment, theory or it simply is an axiom?
- 315
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310
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Isn't a rotation just a sum of many translations?
If the world is (really or hypothetically) made of elementary, point-particles, then it's there such a thing as rotation?
Point particles by definition can't rotate around themselves. The only ...
- 3,002
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65
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Is there a name for linear/homogeneous Galilean transformations?
In Special relativity, the transition charts are Poincaré transformations and linear/homogeneous Poincaré transformations are called Lorentz transformations. (I distinguish between affine ...
- 1,911
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2
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79
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Reference request - book on Euclidean space and rigid body kinematics
Ideally, I'd like a comprehensive book that encompasses both subjects: it builds the notion of "space" as related to our physical world (no relativity, though) from the ground up, giving it ...
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1
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272
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Galilean Symmetry of Newtonian Mechanics
So for the equations of motion to be symmetric about a transformation from $(t,x)$ to $(\tau, y)$, the following must be true (for Newtonian mechanics):
$$m \frac{d^2 x}{dt^2} = f \left( x, \frac{dx}{...
- 21
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2
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564
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Is angular momentum conservation Galilean invariant?
Suppose I have a system of particles with constant total angular momentum $\mathbf{L} = \sum_a m_a \mathbf{r_a \times v_a}$ in frame K. If frame K' moves with velocity $V$ with respect to K and their ...
- 2,020
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198
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Why is vector notation not used in the velocity formula (Galilean Transformations)?
First of all, I'm not that good at physics. This question has to do with a physics course I'm taking at a maths school.
With that said, I am currently learning about the Galilean transformations and I'...
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Is kinetic energy relative or absolute? [duplicate]
I only can think of kinetic energy as absolute. I know velocity is relative but I can't see kinetic energy as being relative because that would violate energy conservation. For example, if in some ...
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2
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Question about relative motion from "A Brief History of Time" [closed]
I read this example in Stephen Hawking's A Brief History of Time:
If one sets aside for a moment the rotation of the Earth and its orbit round the Sun, one could say that the Earth was at rest and ...
- 1
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9
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What is the connection between mechanics and electrodynamics that makes it necessary for both of these to obey the same principle of relativity?
Mechanics obeyed Newtonian relativity (faithful to Galilean transformations) before Einstein.
Einstein formulated Special relativity (faithful to Lorentz transformations), and Maxwell's equations ...
- 1,039
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162
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Formulating Conservation of Energy in Galilean Spacetime
Some background to my question (Galilean spacetime).
The notion of Galilean spacetime is defined at the beginning of Arnold's book on Classical Mechanics. It is a mathematical structure that captures ...
- 404
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2
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3k
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Is Newton's law really invariant under Galilean transformation (for velocity-dependent Lorentz force)?
Consider the motion of a charged particle of charge $q$ and mass $m$ from two different inertial frames $S$ and $S'$ connected by Galilean transformation equation ${\vec r}'={\vec r}-{\vec V}t$. This ...
- 12.3k
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2
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70
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Can distance be relative in Galilean relativity?
In case 1 the A travels the distance D while traveling from X to Y.
In case 2 the velocity of A according to Sam will 'a' and distance travelled by A will be greater than D because the wall Y is also ...
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4
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Is acceleration absolute and if so, how can we measure it?
A person standing on a uniformly moving car can never know (without looking outside, or at the speedometer) whether the car is at rest or in motion at a uniform nonzero velocity w.r.t earth. However, ...
- 12.3k
4
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Newtonian quantum gravity
Can someone give me reference about Newtonian (non-relativistic) quantum gravity like unifying Newtonian gravity with quantum mechanics?
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Dummy variables and Galilean Invariance
I've faced a small doubt, and I was hoping someone could verify this for me.
According to Galilean transformation, consider $2$ frames - $S_1$ and $S_2$ moving relative to each other. $S_1$ is at rest,...
- 1,853
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5
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132
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If motion relative to a frame of reference is purely relative, how do we account for the work done to move relative to the frame of reference?
I get the idea that everything is in motion, and there's no absolute reference frame for everything.
But when we consider local events, like a train passing through a town, I have trouble accepting ...
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0
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38
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Interaction forces always depend on positions only through the distance, therefore conservative?
Suppose that two point masses $A_1,A_2$ are in interaction with each other, resulting in forces $F_1$ (acted upon $A_1$) and $F_2$ (acted upon $A_2$). Let $\bf{x}_1$,$\bf{x}_2$ be their respective ...
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What is the symmetry group of Mach's spacetime?
Newtonian spacetime can be modeled as a geometric object $M$ (affine space or manifold with connection with an absolute time function etc. etc.) that is symmetric under the action of the Galilean ...
- 381
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Right way to define vectors under Galilean transformations?
This two questions: Vectors under Galilean transformation and Galilean transformations of velocity seem to tackle the issue but one was closed and the latter did not refer to vectors.
To me a vector ...
- 5,816
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Why isn't time reversal a Galilean transformation?
I'm a mathematician learning physics from scratch, starting from Newtonian mechanics. As far as I understand, Galilean transformations are defined as transformations of space-time that transform from ...
- 404
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2
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76
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Galilean's principle implies independence of time and dependence on relative distance
Suppose a system of particles $q_1,\ldots,q_N$ of masses $m_1,\ldots,m_N$ that follow the equations of motion
$$m_j\ddot{q}_j=f_j(q_k,\dot{q}_k)$$
in an inertial frame and satisfy the Galilean ...
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How is Newton's first law of motion different from Galileo's law of inertia? If the two are the same, then why is the first law named after Newton?
Galileo's law of inertia (at least what I've learned) is
"A body moving with constant velocity will continue to move in this path in the absence of external forces".
And Newton's first law ...
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