# What is the notation for angular distance travelled?

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1. Feb 12, 2015

### AlbertE97

What is the notation for the angular distance travelled by an object moving in circular motion?

s is for regular distance (m,ft,inches, etc.).

What I want is some x to be the distance in either degrees or radians.

How should I call that x?

2. Feb 12, 2015

### Shinaolord

I would just use $\theta(t)$ and defined it as the total amount of radians that the object has traveled. In your case of circular motion, I would have it be that angle away from its original starting point, $\theta_0$ if $\theta(t) \in [-2\pi+\theta_0\leq\theta(t)\leq 2\pi-\theta_0 ]$. Only include the $\theta_0$ if you are measuring the angle from the origin. If you aren't, and you're measuring the angle from $\theta_0$,it's just $[-2\pi\leq\theta(t)\leq2\pi]$

BUT
If $\theta(t)\notin [-2\pi+\theta_0\leq\theta(t)\leq 2\pi-\theta_0]$which means your not restricting it to one full revolution, than I would say it is the $\textbf{TOTAL}$ angle traveled by the object in time t. The comment about $\theta_0$ being included or not from above applies here as well. (The part about measuring from the origin or $\theta_0$)

Last edited: Feb 12, 2015
3. Feb 12, 2015

### Shinaolord

4. Feb 12, 2015

### AlbertE97

It'll suffice. We'll see if anyone has seen different notation though.

5. Feb 12, 2015

### Shinaolord

You can really use any notation you want, as long as you define what you're doing. For example I could use any of the following ( or anything else, really) for what we are describing, as long as It's stated somewhere.
$\phi(t)\\ \pi(t)\\ \epsilon(t)\\ \zeta(t)\\ A(t)\\ Q(t)\\ \eta(t)\\ \text{etc.,}$

But I don't think that's what you mean. Typically for angles you usually see either $\phi\\ \text{or}\\ \theta$, which are known as phi and theta, as you may know.

Last edited: Feb 12, 2015
6. Feb 13, 2015

### dean barry

This may help:

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