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Questions tagged [inertial-frames]

A specific reference frame that describes its coordinates in a manner that does not depend on time and is isotropic.

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Special relatvity

I am stuck on the following relativity problem: A body travels along the $X$-axis of an IF $S$ with velocity $v$. The $S$ observer emits a monochromatic pulse of light towards the body. The pulse ...
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1answer
42 views

Why doesn't the coriolis force cancel out when a ball is thrown up?

The question is to calculate the lateral displacement of a ball due to the coriolis force once thrown up and allowed to come back down. The initial equation to work with is $\ddot{x} = -2\omega \dot{...
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1answer
28 views

Terminology: can I use the world “comoving” to describe a reference frame in which a certain object is at rest?

Here a question about terminology. Suppose I have a particle that is moving at velocity $\beta$ in the observer (or laboratory) frame. Now, is it appropriate / legitimate to describe the frame in ...
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2answers
47 views

Conservation of momentum in different reference frames

Does the total momentum of a system in a given inertial reference frame have the same numerical value in other inertial reference frames?
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Lorentz transformations: Distance vs “retarded distance”

Suppose I have a charge situated at rest in one inertial coordinate system. The field of that drops inversely with the square of the distance. If I perform a Lorentz boost where v^2«c^2 (not ...
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Is speed of light constant in every inertial reference frame, or does it just seems constant for observers? [on hold]

Here is an hypothetical experiment. (I already used this experiment in previous question but the question was diferent) : Let's call k the distance travelled by light in 1 second We have two ...
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2answers
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A fictitious force in an orbiting frame of reference that is not rotating

Say we have an inertial frame of reference where there's a motionless star at the center and a planet is in circular orbit around it. We further assume that the planet is not rotating in the inertial ...
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1answer
38 views

Centre of mass problem

I came across a problem where there was an ice and tray system. The system was placed in a gravity free hall. After the ice melted the shift in centre of mass was to be found. But the answer is 0. Is ...
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1answer
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Is this a right approach to show that $\partial_{\mu} \phi \partial^{\mu} \phi $ is Lorentz Invariant?

When trying to convince myself that $\partial_{\mu} \phi \partial^{\mu} \phi $ is Lorentz Invariant, I stumbled upon this approach: The last equation should read - $\partial_{i} \phi \partial^{i} \...
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2answers
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What exactly is the meaning of length contraction? [duplicate]

Let's say a train of length $L$ (wrt ground) is standing on rails which have markings for every femtometre (or even smaller units). Now if someone takes a photograph and measures the distance between ...
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1answer
22 views

When do we illustrate inertial forces on inertial frames of reference?

I came across two practice questions wherein an object was attached to an accelerating vehicle, yet only one of these cases required an inertial force to be illustrated on the object's free body ...
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1answer
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What if you recorded the point of view of someone traveling at the speed of light? [closed]

According to the theory of relativity, the rate at which time passes is relative in accordance with speed. They say for example that if your twin gets in a rocket and flies to another planet at close ...
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1answer
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Elastic collision respect to a CM frame [closed]

Two particles, m1 and m2 collide one-dimensionally, if the collision is elastic. show that with respect to the cm frame, the particles reverse their velocity directions, maintaining the magnitudes.
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1answer
59 views

Will tidal effect make physics laws different?

I was reading Wheeler & Taylor's Spacetime Physics. The authors mentioned about tidal effect, as well as all physics laws are same in free-float frame. I am left wondering if tidal effect will ...
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0answers
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Frame of reference coordinate notation [closed]

Let’s take a simple example. I believe I , X, am stationary. Two objects, A and B, are moving away from me in one dimension each at constant but different velocities. What is the simplest and ...
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1answer
37 views

Rapidity in 4-vector Transformation

In Lorentz transformation we have a concept of rapidity as related to boost. Rapidity is defined as a hyperbolic angle α such that $$\tanh(α)=v/c .$$ This further defines a matrix for Lorentz ...
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2answers
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Is this relativistic mass?

I have seen in a lot of places in here clearly stating that relativistic mass is outdated, that we can make do just fine with the concept of invariant mass,etc. But I've also seen people saying that a ...
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Special *set* of inertial frames in an EM field?

Just looking for confirmation of my understanding of the Wikipedia article on classification of electromagnetic fields: The article states that in the case where $E\cdot B = 0$ and $E^2-B^2 \not= 0$...
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Newton's first law

Which statement about an object moving in a straight line through air is correct? (A) When it accelerates, the resultant force acting on it is zero. (B) When it moves at a steady speed, the air ...
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Spacetime diagrams and their interpretation

Recently started an introductory course of relativity, and started learning about space time diagrams. I couldn’t figure out what are the uses of a spacetime diagram as an alternative to Lorentz ...
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2answers
128 views

Problem with speed of light

I constructed a thought experiment, can't figure the answer. Two long (say $1\ \rm{km}$ long) railway cars are on parallel east-west tracks in a zero gravity environment. Each car has a light source ...
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The Lagrangian and inertial reference frames [duplicate]

From my understanding, my instructor told me that in order to use the Lagrangian, defined as $$L \equiv T - V,$$ to find the equations of motion via the Euler-Lagrange equations, the generalized ...
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2answers
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Lorentz transformation of a Weyl Spinor?

A left handed Weyl Spinor belongs to the $(\frac{1}{2},0)$ representation of the Lorentz group. So given the Spinor, the unitary representation of the Lorentz transformation should look like $\exp{iA\...
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1answer
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What is the physical argument for $d(G)_s = d(G)_b + d(G)_{rot} \quad ?$

In the book of Goldstein, Classical Mechanics, at the end of the page 171, it is stated that A relation between the two differential changes in $G$ can be derived on the basis of physical ...
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3answers
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Inertial frames?

This is from a book. A traing is moving on earth. A ball is sitting at rest (relative to the train) on the floor of the train which is moving at constant velocity relative to a tree. If the ...
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0answers
30 views

Velocity addition formula derived from velocity boosts

I understand the derivation for the equation the velocity in a boosted frame by taking the boosts of the differentials such that: $v'^{\mu}= \frac{dx'^{\mu}}{dt'} $ where $x^{\mu} = \Lambda^{\mu}_{\, \...
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3answers
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Defining what it means for a reference frame to move with a velocity $\mathbf{u}$ with respect to another

In describing a Galilean transformation, for example, one might say that if a reference frame $S'$ is moving at a velocity $\mathbf{u}$ with respect to $S$, then an object traveling at a velocity $\...
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1answer
53 views

Does special relativity causes magnetism? [closed]

And if yes, according to amperes law when the magnetic force beetween two current-flowing conductors the force is in linear reverse connection beetween the distance and the force, but if magnetism is ...
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1answer
82 views

How do time-like separated points preserve temporal ordering under orthochronous Lorentz Transformations?

How do time-like separated points preserve temporal ordering under orthochronous Lorentz Transformations? This question has already been asked in this Phys.SE post but I want to derive this result in ...
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1answer
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The ladder paradox - with equal lengths

Take the usual ladder paradox in special relativity, but this time the ladder and the barn have the same length, at rest. Since each one of them contracts when viewed in the rest frame of the other, I ...
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1answer
48 views

Picking the Right Reference Frame

A space vehicle travelling at $3860 \ \text {kmph}$ w.r.t Earth sends its exhausted rocket motor backward with a speed of $125 \ \text{kmph}$ w.r.t the command module. The mass of the rocket motor is $...
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1answer
41 views

How to determine particle energies in center of momentum frame?

I want to show for the following process that, except for the angle $\theta$, all momenta and energies are fixed by energy-momentum conservation. Namely: $$p_A=\frac{1}{2\sqrt{s}}(s+m^2_A-m^2_B\space,...
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1answer
78 views

What motivated Einstein's postulate on the speed of light? [closed]

I know that there are several experiments (conducted after Einstein's formulation of Special Relativity) that confirm to some extend Einstein's postulate that nothing can travel faster than light. But ...
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2answers
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Is Einstein's train-lightening thought experiment consistent with Special Relativity? [closed]

Einstein’s train-lightening thought experiment contains only inertial motion so SR says we can ascribe relative motion and relative rest to either reference frame. Although it is not stated in the ...
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What creates the physical difference in ageing when travelling close to the speed of light? [duplicate]

I probably have a fundamental misunderstanding, so correct me if I'm wrong. When travelling close to the speed of light, movers experience time dilation, which is what results in the phenomenon of ...
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1answer
128 views

Is there a “special” inertial frame determined by the value of E and B at a point in an EM field?

Given the facts that $(E^2 - B^2)$ and $(E\cdot B)$ are Lorentz invariants of the EM field, and that the energy density $(E^2 + B^2)$ is not invariant, it seems that at each point in an EM field there ...
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1answer
79 views

An invariant for transformations of Lorentz

Exist a physical demonstration why $$E^2- p^2c^2 =m^2c^4=E'^2- p'^2c^2 $$ is an invariant for transformations of Lorentz? N.B.: $m$ is mass; $E$ is the energy and $p$ is momentum in the frame $\...
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1answer
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Same energies are transferred to 2 objects. But they gain different amounts of energy. Where is the mistake?

Situation #1. In space, an object is moving with a constant velocity in an inertial reference frame. The object is connected to a winch (winch “A”) with a rope. Winch “A” is in front of the object, ...
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Do I have to know the General Relativity theory to understand the concept of inertial frame?

I have read answers on this site as well as the Wikipedia article, but they all add to the confusion. Some people suggest that a freely falling frame is an inertial frame. I learnt in classical ...
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Inertial and non-inertial reference frames

My book states that: A reference frame attached to earth is not inertial because it is revolving around the sun and it is rotating about its own axis. Don't we need a specified observer's frame ...
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4answers
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Where is the mistake in this reasoning? [closed]

2 identical objects are moving with different constant velocities. Then, in turn same forces act on them for some period. Both times, the same amount of energy is used to produce those forces. As the ...
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4answers
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Why doesn't a ball thrown upwards fall behind us if we're moving forward?

If we consider ourselves traveling in a bus and if we a throw a ball upwards, the ball should fall behind us according to law of inertia, right? If so why doesn't the ball always fall behind us each ...
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1answer
31 views

Galilean transformation and differentiation

Given $x=x’-vt$ and $t=t’$, why is $\frac{\partial t}{\partial x’}=0$ instead of $1/v$? $t$ seems to depend on $x’$ because if $t$ changes, $x’$ changes. Also, in this problem, $dx=dx’$ as well, but I ...
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2answers
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Trouble deriving the Lorentz transforms

After separately arriving at the two equations $x'=\gamma(v^2)(x-vt)$ and $t'=\phi(v^2)(t-\frac{vx}{c^2}$). Where $x'$ and $t'$ are the coordinates a moving observer ascribes to events. I had to show ...
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How is time “homogeneous”?

My book$^1$ states: Let's consider a clock moving freely over a curve such as: \begin{equation} \frac{dx^i}{dt}=\text{const} \tag{1.20} \end{equation} We define the proper time $\tau$ as the ...
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1answer
28 views

Signs in relative vector addition

So I know the formula for relative vector addition is $$w = \frac{v-u}{1-\frac{uv}{c^2}}.$$ How do I chose when to use this formula or its inverse transformation for solving vector addition problems ...
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1answer
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Recordings of journey traveling near speed of light

If you had two identical video cameras and started recording synchronized atomic clocks recording at the same speed and you put one on the spaceship and sent it out traveling at 99% of the speed of ...
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1answer
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Is a reference frame fixed (without rotation) on a precessing gyroscope an inertial frame of reference?

Let's say we put a human in a closed chamber which is going around a certain point at distance d from its center of mass at some angular velocity w. The centrifugal force on a human will be w squared ...
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1answer
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Train and lightning bolts: why the time difference does not depend on the position of the moving person?

So imagine two lightning bolts hit the ground, simultaneously to a stationary observer. There is also a person on a train traveling to the right at a constant velocity. I know that if he started in ...
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4answers
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Is there a frame of reference in which I was born before I was conceived?

I'm struggling to understand the relativity of simultaneity and position. If my conception and birth are separated by time but not space, a frame of reference in which my birth and conception are ...