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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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Relativistic Mass when Viewed from Different Frames of Reference

I understand relativistic mass and the equations underpinning it. My question deals with how to calculate relativistic mass when an object is viewed from different frames of reference. Consider a ...
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1answer
34 views

Conservation of kinetic energy in two dimensional elastic collisions

I have a question where two particles collide with each other in a non central way. Mass of particle 1 ($m_1$) is $1\text{kg}$ and its velocity $v_1$ is $5\text{m/s}$ (moving along the x-axis) ...
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What if a spaceship going half the speed of light turned on its headlights in both directions?

If the spaceship, travelling at c/2 were to turn on only its forward facing headlights, then after one second (relative to us, the stationary external observers) we would see that the ship has moved ...
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2answers
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Rotational Dynamics equation from non inertial frames

Suppose instead of writing torque = Icalpha from the centre of mass, I want to write it from another non inertial frame. I know L = Lcm + RxPcm from any other frame , so if Idifferentiate it wrt time ...
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Difference betwee $(d\vec r/dt)_{fixed}$ and $(d\vec r/dt)_{not~fixed}$

$[![Picture ~from ~http://www.astro.uwo.ca/~houde/courses/PDF%20files/physics350/Noninertial_frames.pdf][1]][1]$ From the picture above, the set of coordinates $x_i$ are the ones that are not fixed ...
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Is Earth an inertial reference frame?

Is earth considered as inertial frame? i was confused because we learned about coriolis effect. We know that earth spins therefore coriolis effect should take place . But does it have minimal effect ...
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1answer
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Relativistic Doppler Effect - calculate frequency $f'$ and $f$ in references $S'$ and $S$

Considering that $S$ (fixed) and $S'$ are inertial references which coincides when $t=t'=0$ and their coordinates $(ct,x,y,z)$ and $(ct',x',y',z')$ are related by Lorentz's transformations, calculate ...
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If I walk and you stand still, do you get older than me faster?

I was watching a video from Aurelien Barrau about relativity and time. As he was talking to the audience, he said that since he was walking on stage, he was ageing slower than people sitting in the ...
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1answer
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Criteria on good inertial system approximation

I'm currently wrapping my head around Newton's First Law. I think I start to get a basic understanding on the meaning of this law in terms of "the existence of inertial system". Basically my ...
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2answers
86 views

Why aren't shape of galaxies depicted as a funnel?

Let's say if a galaxy is moving, shouldn't it be shaped like a funnel? I am saying this because it would take considerable time for the outermost star to know that the center of gravity has shifted. ...
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Lagrangian method for finding Lorentz transformation [closed]

Consider a very general case: one reference system (x', y', z') is moving away from another fixed system (x, y, z) with constant speed $v$ (like in the fig. a little bit below). Normally, using the ...
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Operators, gamma matrices and Lorentz invariance

In class, we have define the following operator: $$\Pi_{\pm} = \frac{1 \pm \gamma^0}{2} \tag1$$ Where, $\gamma^0$ is the usual first gamma matrix in Weyl representation. Applying it to a 4-...
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Conservation of Momentum and Friction in an Inertial Frame

Let us suppose that a rectangular, tabular body is moving in translational motion through space at a constant velocity and the surface of it has a low coefficient of static and kinetic friction. ...
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2answers
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Minimum separation from the spacetime interval

I've been working through invariant spacetime interval questions recently, and I came across a question in my lecture notes where; $$\Delta s^2=\Delta x^2 -(c\Delta t)^2 > 0 $$ Now it is clear to ...
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10answers
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How does an isolated body in deep space 'know' it's rotating? [duplicate]

We can imagine an object floating in the known universe, maximally distant from any other large mass. Maybe it has been there since coalescing after the big bang. What physical phenomena tell it ...
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2answers
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If the speed of light is a limit, is there a way to tell which direction we are moving through space and how fast?

Say two photons start at point A, and go in opposite directions. They will be traveling apart at 2x the speed of light correct? So if this limit is how fast you are able to travel through space (and ...
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1answer
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Why the speed of light is independent of the relative motion of observer? [duplicate]

As we use Lorentz transformation equation to relate velocity of particle measured by observer which is in frame s this frame is in relative motion having some velocity to that particle so Why the ...
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5answers
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Is relativity really relative?

Because of the relativity of linear motion, you can't tell the difference between whether your spaceship is moving and the stars are standing still or whether you're still and the stars are moving the ...
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2answers
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Can two electron moving in opposite direction move faster than light? [duplicate]

Suppose we are moving two electrons in opposite direction both having a speed of 1.6e8 meter per sec.When they will cross each other then their relative velocity will be 3.2e8 ms_1.Isn't it faster ...
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2answers
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Particle in a gravitational field moving at constant speed in some inertial frame

While working on an unrelated problem I found an interesting result which I presume must already be known, but I cannot find any reference to it. It is the following: Consider a small particle P ...
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3answers
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Friction and Work in Inertial Reference Frames [duplicate]

Say a train is moving in the positive $x$-direction at 100 meters per second with respect to the ground frame. Now let's say someone is pushing a large box in one of the cars of that train in the ...
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Question about inertial frames and geodesics

Consider the following text: In Newtonian Mechanics the first law is given by: $$\Big[m \Big(\frac{d^{2}x^{a}}{dt^{2}} + \Gamma^{a}_{bc}\frac{dx^{b}}{dt}\frac{dx^{c}}{dt}\Big)\Big]\frac{\partial}{\...
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5answers
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Inertial and non-inertial frame

How to define an inertial frame of reference mathematically? I want a definition with proper chosen coordinate axis which will help me to differentiate it with the non inertial ones. I have been ...
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2answers
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Doesn't the slowing of time when travelling at almost light speed create a paradox with an observer? [duplicate]

Disclaimer: I am extremely new to this and have no proper knowledge of this subject at all, this is just an idea that I had which I want to properly understand. I don't have any knowledge of necessary ...
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Transformation of opening angle in different frame of rerefence in special relativity

I have to find the minimum opening angle for the decay $\pi^0 \rightarrow \gamma \gamma$ given the energy and rest mass of the $\pi^0$. My question is that: since the center-of-mass frame's opening ...
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Which observer measures proper time in the twins paradox?

I know that proper time is defined as the time which the clock moving relative to that observe shows. That is, a clock attached to observer A will always be As proper time. I also understand that this ...
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Clock of photon demon [duplicate]

If a photon was a small small guy, and he is moving at the speed of light in the vacuum space with a clock, will his clock stay still forever? If yes, Mr. Photon is basically "frozen"? When Mr. ...
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Galilean transform wave equation differentials

We have the wave equation \begin{equation} -c^2 dt^2 + dx^2 = 0 \end{equation} With typical Galilean transform: \begin{equation} \left\lbrace \bar{x} = x - v t \atop \bar{t} = t \right. \end{...
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1answer
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Gravitational potential energy with both bodies moving [closed]

When deducing the formula for the gravitational potential energy of one body in relation to the gravitational force of another body, my teacher assumed that one body was standing still. I tried ...
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1answer
168 views

The derivation of the Lorentz transformation: addition of distances

In the derivation of the Lorentz transformation, one has a reference frame, $S$, at rest and another, $S'$, moving away at constant speed $v$. At time $t$ there is an event at a point $x$ in $S$. The ...
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6answers
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If photons don't experience time, does that mean time is a consequence of mass? [closed]

If photons don't experience the passage of time because they have no mass, does that mean time is a consequence of mass? To me that's a profound conclusion yet not one I see printed. Is it right?
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3answers
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Why does speed of light have to be constant?

My question is not about why speed of light has a particular constant value which has been sufficiently addressed in other questions on SE already. I want to know whether the fact that speed of light ...
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0answers
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Is the speed of light constant regardless of the frame of reference? [duplicate]

I'm confused; I understand that the speed of light is constant for any observer, and that heading towards or away from a light source only causes it to blue or red shift (increase or decrease ...
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2answers
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Are these collisions equivalent?

Similar to the question if two cars with a velocity of 50 mph each colliding is the same as one car colliding with wall at 100 mph, I was wondering if the same amount of energy is produced when ...
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6answers
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Is the relative speed of light really invariant, irrespective of the motion of the observer? [closed]

If 3 observers are on a planet which 100 light years from a star, and the star goes supernova, if one observer moves towards the star and one moves in the opposite direction, each observer will see ...
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4answers
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When electron moves constantly, it's electric field moves with it instantly?

When electron accelerates, there occurs a propagated ripple on it's electric field. But when it moves constantly, does the field "follow it", i.e. changes instantly? How does it deals with the fact ...
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1answer
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Invariance of spacetime interval in special relativity: linearity

I'm trying to understand which assumption are necessary to prove the invariance of the spacetime interval $$\Delta s^2=c^2\Delta t^2-\Delta \mathbf{x}^2$$ in special relativity. The postulates of ...
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What's the relationship between reduced mass and the total energy of collisions in the lab and center of mass frame?

Is there a relationship between reduced mass and the total energy of collisions in the lab and center of mass frame? If so, could someone explain how it is related?
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What are the axis of collisions in the laboratory and center of mass frame?

This may be a silly question. I was asked, "what are the axis of collisions in the lab and center of mass frame?". My first thought was that that the colliding masses are on the same axis for both ...
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1answer
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Speed of light, can it be not constant? [duplicate]

What if we switch on a flashlight while travelling at the speed of light (we are travelling in vacuum, in a straight path)? What will happen and what will be the speed of light from the flashlight? ...
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1answer
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Why is the laboratory frame energy always greater than the center of mass frame energy for collisions? [duplicate]

I looked through lots of sources to answer the question, 'Why is lab frame energy (total energy) always greater than the center of mass frame energy?' Many of them provided lots of mathematical ...
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3answers
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Why is the laboratory frame energy always greater than the center of mass frame energy?

I have been looking for an answer to 'Why is the laboratory frame energy always greater than the center of mass frame energy during collisions?'. A lot of resources provided mathematical explanations....
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4answers
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What's the speed of light when viewed from the side?

Suppose a pulse of light is sent from $A$ to $B$ in a rigid triangle $ABC$. While the pulse is moving from $A$ to $B$, what is it's velocity relative to $C$? The special character of the photon among ...
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1answer
44 views

Doppler effect in light (Observer moving away from source)

I understand this intuitively and can picture it in my head, but when I do it on paper, the result is a sign difference that I cannot understand According to this diagram the wavelength = ct-vt = t(c-...
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1answer
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Should the rest frame of a lab positioned on a gravitating body be considered an inertial frame in special relativity or not?

In Newtonian Mechanics, the rest frame of a lab on the Earth is considered to be (approximately) an inertial frame. The fact that a thrown ball is not moving on a straight line corresponds to the ...
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Can we decompose a general Lorentz boost in a rotation followed by three boosts along the coordinate axes?

$\newcommand{\betabold}{\boldsymbol{\beta}} \newcommand{\xbold}{\boldsymbol{x}} \newcommand{\ebold}{\boldsymbol{e}}$ For $\betabold\in \mathbb R^3$, with $0<|\betabold|<1$, let us denote the ...
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2answers
76 views

Equivalence principle and local inertial reference frames

Local inertial reference frames are defined as follows: Pick a set coordinates for the manifold (assuming the manifold can be described by global coordinates) $\{x^i\}$ such that $g(p) = \eta$ is the ...
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3answers
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How to distinguish force from accelerating frame of reference?

So in this question Is this the reason why acceleration is said absolute?, author asks is his reasoning about absolute acceleration right, and he concludes that we can measure absolute acceleration of ...
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5answers
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Paradox in the definition of work [duplicate]

I'm trying to understand the Oberth effect and came across this paragraph that seems crazy to me: when the rocket moves, its thrust acts through the distance it moves. Force multiplied by distance ...