Understanding Uniform Circular Motion

Now, if you look up at your fan, you know that, there are many points at different distances from the center. Right? But you know, if I rotate that fan, all of them will cover a rotation together. Right? One of them will not go in front or behind the other. We have a way of saying this. What do we call it? We say that all of them have the same angular velocity – omega. Now you know all of them have the common or constant omega. But can this omega itself can change with time? Yes. Right? If you look up at your fan when its switch off, what is that common omega for all the points? Zero. None of them are covering anything and once you switch it on – what happens? They start covering a very-very small angle for a given time, which means the omega is very small to begin with and as time goes – as the fan starts going faster – which means it has a larger omega. Eventually the fan reaches its final velocity and after that it will not increase its speed. So at that time if you look, what’s happening? Not only is the omega for all the points is common, the omega itself with time is not changing anymore. Till then it was increasing and after that it reaches a constant value. Now if you look up at the fan, it covers one rotation – let’s say in a second – and second rotation also will take one second and so on. Now this special case where the omega is not changing with time and remains a constant is called uniform circular motion. And why is it special? Let’s find out.