Which one of the following is the correct relation between frequency $f$ and angular frequency $\omega$?
[amp_mcq option1=”$f = \pi\omega$” option2=”$\omega = 2\pi f$” option3=”$f = 2\omega/\pi$” option4=”$f = 2\pi\omega$” correct=”option2″]
This question was previously asked in
UPSC NDA-1 – 2017
Angular frequency ($\omega$) represents the rate of rotation or oscillation in terms of angle per unit of time (usually radians per second), measured in rad/s.
One complete cycle or revolution corresponds to an angle of $2\pi$ radians. If $f$ cycles occur per second, then the total angle covered per second is $f \times (2\pi)$ radians.
Therefore, the angular frequency $\omega$ is related to the frequency $f$ by the equation:
$\omega = 2\pi f$