Tag Archives: Speed

Problem 2-6: The average speed and average velocity of a spinning helicopter blade

Advertisements

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?

Advertisements

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)
Advertisements
Advertisements

Problem 2-5: The Earth’s average speed and velocity

Advertisements

PROBLEM:

(a) Calculate Earth’s average speed relative to the Sun.

(b) What is its average velocity over a period of one year?

Advertisements

SOLUTION:

Part A

The average speed of the earth is equal to the distance traveled divided by time.

\begin{align*}
\text{Average speed of the Earth} & =\frac{\text{Distance Traveled}}{\text{Total time of Travel}} \\ \\
& =\frac{2\pi \text{r}}{\text{t}} \\ \\
& =\frac{2\pi \left(1.50\times 10^{11}\text{ m}\right)}{365.25\:\text{days}}\times \frac{1\:\text{day}}{24\:\text{hours}}\times \frac{1\:\text{hour}}{3600\:\text{sec}} \\ \\
& =2.99\times 10^4\:\text{m/s} \ \qquad \ \color{DarkOrange} \left( \text{Answer} \right)
\end{align*}

Part B

After a period of 1 year, the planet Earth has already returned to its original position with respect to the Sun. This means that we do not have any displacement. Therefore, the average velocity is zero.

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