# Frequency and Angular Frequency Frequency, typically denoted as $f$ , measures the number of cycles (or oscillations) that occur per unit of time. It is expressed in hertz (Hz), where one hertz equals one cycle per second. Frequency tells us how often an event repeats itself over a set period of time. For instance, if a pendulum swings back and forth 60 times in one minute, its frequency is 60 cycles per minute or 1 Hz. Angular frequency, denoted as \omega , measures the rate of rotation or angular displacement per unit time and is expressed in radians per second (rad/s). Angular frequency is used when discussing phenomena that involve rotations or circular motion, where it is useful to express changes in terms of angles. The relationship between angular frequency and frequency is given by: $\omega = 2 \pi f$ Here, $\pi$ (approximately 3.14159) represents the mathematical constant $\pi$, which relates the diameter of a circle to its circumference. This formula comes from the fact that one complete cycle around a circle corresponds to an angle of $2 \pi$ radians. In essence, while frequency counts how many times something happens per second, angular frequency measures how many radians are covered in that process per second, tying the concept more tightly to rotational and oscillatory contexts. --- Date: 20240518 Links to: [Physics](notes/Physics.md) Tags: References: * []()