The RPM of the fan is 2400.
The angular velocity can be determined as,
[tex]\begin{gathered} \omega=\frac{2\pi N}{60} \\ =\frac{2\times\pi\times2400}{60} \\ =80\pi\text{ rad/s.} \end{gathered}[/tex]The time period can be determined as,
[tex]\begin{gathered} T=\frac{2\pi}{80\pi} \\ T=\frac{1}{40} \\ T=0.025\text{ s} \end{gathered}[/tex]Thus, the required time period is 0.025 seconds.
The frequency can be determined as,
[tex]\begin{gathered} f=\frac{1}{T} \\ =\frac{1}{0.025} \\ =\frac{1000}{25} \\ =40\text{ Hz} \end{gathered}[/tex]Thus, the required frequency is 40 hertz.
