Chapter 4.1, Problem 77E

To determine

To explain: how the speed of the tips of the blades changes when a fan of greater diameter is installed on the motor.

Answer to Problem 77E

Speed increases.

Explanation of Solution

Concept Used:

If $\theta$ is the angle (in radian) corresponding to the arc length s , then the linear speed v is:

  $v=\frac{s}{t}$

The arc length s is given by,

  $s=r\theta$

The linear velocity is given by,

  $\begin{array}{c}v=\frac{s}{t}\\ =\frac{r\theta }{t}\end{array}$

So, it can be observed that the linear velocity is proportional to the radius.

So, if the radius increases, then the linear velocity will also increase.