# Tag Info

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 ...
• 103k
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 ...
• 21.4k

### 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 ...
• 490

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 $\mathcal ... 2 votes ### Meaning of general Lorentz transformations I will call these observers$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}$, with the same ... • 1,775 2 votes ### Choice of Generalized Coordinates$ \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 ... • 12.4k 2 votes ### Choice of Generalized Coordinates You are correct that you are going to need some positional generalized coordinates also. I would suggest the distances$along the ramp from some horizontal reference plane, and the distance$t$for ... • 3,190 1 vote ### Choice of Generalized Coordinates I wanted to post my own answer, inspired by that of Refik Mansuroglu. Let$\theta$be the angle down the slope the wheel has rolled and let$\phi$be the counterclockwise angle through which the wheel ... 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. ... • 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 ... • 291 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 ... • 41.1k 1 vote Accepted ### 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 ... • 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^...

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