PROBLEM:

A helicopter blade spins at exactly 100 revolutions per minute. Its tip is 5.00 m from the center of rotation.

(a) Calculate the average speed of the blade tip in the helicopter’s frame of reference.

(b) What is its average velocity over one revolution?

SOLUTION:

Part A

The average speed of the blade tip is equal to the distance traveled divided by the time elapsed.

\begin{align*}
\text{speed} & =\frac{ \text{distance traveled}}{ \text{time elapsed}} \\ \\
& =\frac{2\pi \text{r}}{ \text{t}} \\ \\
& =\frac{2\pi \left(5.00\text{m}\right)}{60\:\text{s}}\times 100\:\text{rev} \\ \\
& =52.36\:\text{m/s} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}

Part B

After one revolution, the tip of the blade is at the same position as it is originally. This means that the displacement is zero. Thus, the velocity is zero.

\text{v}=0\:\text{m/s} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)