All Questions
Tagged with galilean-relativity vectors
11 questions
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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
1
answer
189
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Why not define tensors under Galilean or Poincare transformations?
I have seen vectors (and tensors, in general) defined under rotations,
$$V^i=R^i_{~j}V^j$$
and under Lorentz transformations,
$$V^{\prime\mu}=\Lambda^\mu_{~~\nu}V^\nu$$
where $R,\Lambda$ are the ...
- 12.3k
2
votes
2
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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'...
- 158
0
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1
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85
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Vector calculus of a potential energy formula under Galileo transformation
I'm currently studying MIT OCW 8.20 Introduction to Special Relativity. In pset 1, the following question is being asked: Suppose you have a potential of the form U($\vec{r_1}, \vec{r_2}$) = U(|$\vec{...
- 13
0
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1
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67
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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
1
vote
2
answers
297
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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 ...
- 5,806
1
vote
1
answer
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Effect of relative velocities in time dilation thought experiment
Related
Classical mechanics thought experiment:
We throw a ball upwards with a velocity of $10~m/s$ we know that the ball will fall on ground in 2 seconds.
We throw another ball now with a velocity ...
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1
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1
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284
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Vectors under Galilean transformation [closed]
Acceleration and speed are both vectors. The former is invariant under boosts, while the latter is not. Why are vectors defined solely on the way they change under rotations and not under Galilean ...
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6
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2
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513
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Is Velocity Really a Vector?
In non-relativistic physics, physical quantities $Q$ are characterized by how they transform under a Galilean transformation $g \in \mathcal{G}$.
$$ Q \rightarrow Q' = D[g]Q$$
where $D[g]$ is the ...
- 307
5
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4
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Are vectors truly independent of coordinate systems?
I have been told to think of vectors as existing independent of a coordinate system. This means that the magnitude of a vector should be independent of any coordinate system we choose. Galilean ...
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1
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Calculating relative velocity in three dimensional space
Given two points $\mathcal{A}$ and $\mathcal{B}$ in $\mathbb{R^3}$ whose position and velocity vectors are, respectively:
$$\mathbf{r_A}=\begin{pmatrix}r_{A_{x}}\\r_{A_{y}}\\r_{A_{z}}\end{pmatrix}$$
$$...
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