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7 votes
Accepted

Length Contraction: is $t'$ or $t = 0$?

David Morin is correct. Length in a given frame is defined as the distance between the two ends of an object at the same time in that given frame. So length is a concept that is intrinsically tied to ...
Dale's user avatar
  • 103k
6 votes
Accepted

How do I know if a motion is 1 dimensional or 2 dimensional?

Let's say you have the following motion (the red arrow) It looks 2D on this plot, since its motion changes both the $x$- and $y$-coordinates. However, if you redefine the axes like so: Then the ...
Allure's user avatar
  • 21.4k
5 votes

How do I know if a motion is 1 dimensional or 2 dimensional?

Both you and your teacher can be correct depending on what you mean by "dimension." In everyday experience, we generally consider dimensionality to be the number of independent parameters ...
Roger Yang's user avatar
4 votes

How do I know if a motion is 1 dimensional or 2 dimensional?

One dimensional motion is any kind of motion that happens on a line. There are many ways to define this. For example, you could say that the position vector of the particle is always $\vec{r}(t)=r(t)\...
agaminon's user avatar
  • 1,775
3 votes
Accepted

Choice of Generalized Coordinates

If you want to use Lagrange multipliers as the exercise hints to, you can do the following: Start with an overdetermined parameterization of the system, say using $\left( \theta, \dot \theta, \phi, \...
Refik Mansuroglu's user avatar
3 votes

Meaning of general Lorentz transformations

Let's look at the bigger picture first. A Lorentz transformation maps a set of coordinates $(t,\mathbf r)$ to another set of coordinates $(t',\mathbf r')$. More specifically, if an observer $\mathcal ...
AccidentalTaylorExpansion's user avatar
2 votes

Meaning of general Lorentz transformations

I will call these observers $S$ and $S'$. The condition $\mathbf{r}_{\parallel}=\mathbf{v}t$ implies that $S$ is measuring a point in space that travels with velocity $\mathbf{v}$, with the same ...
agaminon's user avatar
  • 1,775
2 votes

Choice of Generalized Coordinates

$ \def \b {\mathbf}$ The Rotation Matrix between the wheel coordinate system and inertial system is: \begin{align*} &\b R=\b R_y(\phi)\,\b R_z(\theta) \end{align*} form here you obtain the ...
Eli's user avatar
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2 votes

Choice of Generalized Coordinates

You are correct that you are going to need some positional generalized coordinates also. I would suggest the distance $s$ along the ramp from some horizontal reference plane, and the distance $t$ for ...
JAlex's user avatar
  • 3,190
1 vote

Choice of Generalized Coordinates

I wanted to post my own answer, inspired by that of Refik Mansuroglu. Let $\theta$ be the angle down the slope the wheel has rolled and let $\phi$ be the counterclockwise angle through which the wheel ...
Georgy Zhukov's user avatar
1 vote

How do I know if a motion is 1 dimensional or 2 dimensional?

the main thing take away: physics does not care a about your coordinates. So if the thing is moving on: $$ \vec r(t) = t\cos{\theta}\hat e_1 +t\sin{\theta}\hat e_2 $$ thats linear motion in a plane. ...
JEB's user avatar
  • 35.5k
1 vote

Boundary conditions on transition maps on general relativity

There's nothing fancy going on with transition maps. What a mathematician means by a "transition map", in the setting of general relativity, is nothing more or less than a coordinate change ...
Lee Mosher's user avatar
1 vote
Accepted

Invertibility between generalized and actual coordinates

While it is true that you use 3 numbers for Cartesian coordinates, you do not use the full set of triplets. You use the subset that satisfies $x_1^2 +x_2^2 + x_3^2 = r^2$. This subset has two degrees ...
mmesser314's user avatar
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1 vote
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Rotating a system

As for what most people mean when they say rotate the axis - yes, it usually implies keeping all objects in the same points in space, and just using new coordinates to express their position, velocity ...
Ido's user avatar
  • 26
1 vote

Physical meaning of Boyer-Lindquist coordinate

For me, the BL coordinates allow to plot the particle location $ (x,y,z) $ around a Kerr black hole in a Cartesian frame of a static observer: $$ x=\sqrt{r^2+a^2}\sin\theta\cos\phi $$ $$ y=\sqrt{r^2+a^...
Cornelius Fyla's user avatar

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