Chapter 10, Problem 29A

Use the equation $\nu =r\omega$ to explain why the end of a fly swatter moves much faster than your wrist when swatting a fly.

To determine

The reason that the end of a fly swatter moves much faster than the person’s wrist when swatting a fly.

Answer to Problem 29A

It is because distance of the end of a fly swatter is more than the distance of the wrist from the shoulder.

Explanation of Solution

Introduction:

A linear speed $\left(v\right)$ is written in terms of the rotational speed $\left(\omega \right)$ as,

  $v=r\omega$

Where, $r=$ distance from the axis

The rotational speed of the person’s hand, $\omega$ , will be same when swatting a fly. Then, using the above mentioned formula,

  $v\propto r$

Now, the distance of the fly swatter from the shoulder is significantly large than the distance of the wrist from the shoulder. Therefore, the end of the fly swatter moves much faster than the person’s wrist.

Conclusion:

Hence, due to the difference in the distances of the end of the fly swatter and that of the wrist from the shoulder, there is a difference in their respective speeds.