# An object is traveling around a circle with a radius of 2 meters. If in 20 seconds the object travels 5 meters, what is its angular speed? What is its linear speed?

Jan 29, 2016

I found $0.25 \frac{m}{s}$ and $0.125 \text{rad/s}$.

#### Explanation:

The linear speed will be:
$v = \text{distance"/"time} = \frac{5}{20} = 0.25 \frac{m}{s}$
The angular speed is:
$\omega = \text{angle"/"time} = \frac{\theta}{t}$
but...how do we find the angle described by our object????

We know that between radius, $r$, angle $\theta$ (in radians) and arc length $s$ there is a relationship as:
$s = r \theta$
so $\theta = \frac{s}{r} = \frac{5}{2}$rad
Finally then:
$\omega = \frac{\frac{5}{2}}{20} = 0.125 \text{rad/s}$

The two speeds are also connected through the radius as:
$v = \omega \cdot r$...try it!!! :-)