What is the angular frequency of a fan that completes 60 rotations in 3 seconds?

Question

ScanSolve AI Tutor · Accepted Answer

This question asks for the angular frequency of a fan.

Identify the given information.
- Number of rotations ( $N$ ) = 60 rotations
- Time ( $t$ ) = 3 seconds
Calculate the linear frequency ( $f$ ).
Linear frequency is the number of rotations per unit time.
$f = \frac{\text{Number of rotations}}{\text{Time}}$ $f = \frac{60 \text{ rotations}}{3 \text{ s}}$ $f = 20 \text{ Hz}$
Calculate the angular frequency ( $\omega$ ).
Angular frequency is related to linear frequency by the formula:
$\omega = 2\pi f$
Substitute the value of $f$ :
$\omega = 2\pi (20 \text{ Hz})$ $\omega = 40\pi \frac{\text{Rad}}{\text{sec}}$
Select the correct option.
The calculated angular frequency is $40\pi \frac{\text{Rad}}{\text{sec}}$ , which corresponds to option 1.

The final answer is $\text{1. } 40\pi \frac{\text{Rad}}{\text{sec}}$ .

Answer