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### 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

### 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

### 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 ...
• 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

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