An object is traveling around a circle with a radius of 10 cm. If in 20s a central angle of 1/3 radians is swept out, what is the linear speed of the object?
You can do this in two ways.
1. v = d / t
The distance traveled is the arc length swept out. So d = (10 cm)(1/3 rad) = 10/3 cm. This is covered in 20 s, so
$\displaystyle v = \frac{d}{t} = \frac{\frac{10}{3}~cm}{20~s} = \frac{1}{6}~cm/s$
2. Find the angular speed from $\displaystyle omega = \theta / t$ then find the linear speed by $\displaystyle v = r \omega$. It comes out to be the same thing in the end.
-Dan