User:
Arc traveled when rotating
Description 
If you observe a circle, its perimeter will be $2\pi r$, with the radius ($r$). If you have a angle variation ($\Delta\theta$), it represents a fraction of the total circumference, given by the expression:
$\displaystyle\frac{\Delta\theta}{2\pi}$
the distance traveled in a time ($\Delta s$) corresponding to the arc under the angle variation ($\Delta\theta$) which can be calculated as this fraction of the total perimeter of the circle:
For these calculations, it is crucial that the angle is expressed in radians.
ID:(9879, 0)
Arc traveled
Equation
The position the distance traveled in a time ($\Delta s$) in a circular motion can be calculated from the angle variation ($\Delta\theta$) and the radius ($r$) of the orbit using the following formula:
 $ \Delta s=r \Delta\theta $ |
If an object is at a distance equal to the radius ($r$) from an axis and rotates by ($$), which with the angle ($\theta$) and the initial Angle ($\theta_0$) is
| $ \Delta\theta = \theta - \theta_0 $ |
it will have traveled an arc length the distance traveled in a time ($\Delta s$), which with the position ($s$) and the starting position ($s_0$) is
| $ \Delta s \equiv s - s_0 $ |
This arc length can be calculated by multiplying the radius ($r$) by the angle, that is,
| $ \Delta s=r \Delta\theta $ |
.
ID:(5302, 0)