Angular velocity versus Angular Frequency

so I have received a question from Kanpur v's sir could you upload video on YouTube differentiating angular velocity and angular frequency so the two terms angular velocity and angular frequency so wants to find the difference now angular velocity when you say you have a particle going in a curved path or a circular path so this is the situation in which this angular velocity is the relevant word so if you have some origin and then there is some axis some line and you have a particle at some certain time it is here and this angle is Theta and it is rotating it is going so the particle which is somewhere else and then you can ask that what happened to that theta so that theta is increased that theta is changed by angle D theta and if the time taken is DT then you say that D theta DT is the angular velocity so this is when a particle is going on some path and then angle with this line which is fixed line is changing with time and then you say that the particle is rotating and moving in rotational motion and then you define this angular velocity term d theta/dt angular frequency frequency comes when there is something periodic anything periodic like our AC the power which is used in houses though it is AC power so current which is going in your tube light or in bulb so it is an AC so how do you write the current the current is some constant times sine Omega T or cos Omega T like this there is no rotation nothing is rotating no angle is changing theta does not become theta plus D theta is only that you have a wire and then you have a current and the magnitude of the current and the direction of current is changing and I think at any time T the current is given by this so frequency can be of any periodic motion any kind of periodic phenomena not necessarily motion any kind of periodic phenomena you will have frequency how many repetitions per unit time how many repetitions per unit time if you are blinking your eyes very regularly you can ask what is the frequency or sound sound wave the pressure of air changes compression and rarefaction and compression and rarefaction there is no rotation as such there is no rotation no angular velocity involved but yes per unit time these many times you have compression and you have rarefaction so any phenomena which is periodic for that you can define free Quincy so frequency is number of repetitions you can say per unit time so depending on what is that phenomena this this will have different meanings but essentially after how much time it repeats so that is a time period and the opposite in per unit time how many repetitions that is called frequency and it's represented by those kind of phenomena can be represented by this kind of function sine Omega T cos Omega T this kind of function and this Omega and this frequency they are related this is two pi nu the frequency is nu number of repetitions per unit time cycles per second or Hertz so that is frequency and then 2pi times nu is omega which appears in this equation when you describe that quantity as a function of time through an equation which is repeating regularly after a certain time interval you have this kind of equation and this Omega appears here and therefore it's an important quantity this is known as angular frequency so that is the relation between angular frequency and frequency and frequency is won by time period and so on and here is angular velocity where something is actually rotating and some angle is changed and the rate of change of that angle is known as angular velocity and if the particle is going on a circle that is also repetition if the particle is going on a circular with uniform speed then also you can talk of angular frequency because you have frequency you have repetition so you can calculate what is this angular frequency and you also have angular velocity and it may happen that the two have the same value but the meanings are very very different

Channel: H C VERMA

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Id: dZOq8SbR1XQ

Length: 6min 2sec (362 seconds)

Published: Thu Jul 04 2019