Question

A bicycle wheel rotates uniformly through 2.0 revolutions in 4.0 s. what is the average angular speed of the wheel?

Answer 1

FIrst let's convert the angular distance covered by the wheel into radians. We know that 
$1 rev = 2 \pi rad$
Therefore, 2 revolutions correspond to
$2 rev = 4 \pi rad$

The average angular speed of the wheel is given by the ratio between the angular displacement and the time taken:
$\omega = \frac{\theta}{t}$
where in our problem, $\theta = 4 \pi rad$ and t=4.0 s, so the angular speed of the wheel is
$\omega = \frac{\theta}{t}= \frac{4 \pi rad}{4.0 s}= \pi rad/s =3.14 rad/s$