Angular speed and angular frequency use the same variable $\omega $ are there any differences in their interpretation? Explain

Hint: The number of cycles completed per second by an alternating quantity is known as frequency and is denoted by f.in SI system the frequency is expressed in hertz.one hertz is equal to one cycle per second .the number of cycles completed by second =f and time period T=time taken in completing one cycle =\[\dfrac{1}{f}\].

Complete step-by-step solution:
At the glance at above fig indicates that each cycle spans \[2\pi \] radians. Hence, if this quantity is divided by the time period,
Angular velocity is also called an angular frequency vector. angular velocity of the sine function is obtained. Angular frequency is denoted by $\omega $ and is expressed in radians per second.
Angular frequency is the angular displacement per unit time
Angular frequency() is given by:
 $\omega $ = $\dfrac{Angle Turned}{Time Taken}$
$\omega =\dfrac{2\pi }{T}=\dfrac{2\pi }{\dfrac{1}{f}}$
$\omega =2\pi f$Radians per second
In a multipolar machine, the number of cycles completed per second by generated emf is given by the equation f=product of pairs of poles into number of revolutions made per second
$f=\dfrac{PN}{120}$
Angular speed is the measure of how fast the central angle of a rotating body changes with respect to the time.
Angular speed is given as the ratio of total distance converted ($\Theta $) into total time taken (t).
$\omega =\dfrac{\Theta }{t}$ Radians per second
Angular frequency is a scalar quantity and angular speed is also a scalar quantity.
Angular speed and angular frequency use the same variable $\omega $ and both are different.


Note: Students the SI unit of angular speed and angular frequency are the same but they perform different operations in order to differentiate you have to go through definition and their applications. Both angular frequency and angular speed is a scalar quantity. The linear speed is measured in meters per second.