We saw a while ago that circular motion requires a centripetal force, but there is also another interesting feature that comes out from all that going round, and that is that you can do it all again (and again and again ... ad nauseum).
So what we have is a type of motion we refer to as periodic motion. That is motion that repeats itself after a period of time, and most commonly this period of time is constant (ie uniform circular motion, such as an orbit). So you start off at a certain point and then you move before coming back to where you started.
This is sort of obvious when you think about travelling in a circle. And as you can see this is a very simple sort of periodic motion.
Now since going around in a circle involves going through 360° we often describe the motion in terms of the rate at which the angle changes - the angular velocity (ω) if you will. The simplest way to think of this is, like I said, a velocity so we will consider the angle changed divided by the time taken (much like velocity is distance moved divided by time taken) and so we get
- ω = 2π/T
- 2π rad = 360°
- v = 2πr/T
- v = ωr
- s = θr
- a = αr
Now why is all of this remotely important, any one familiar with geometry will note that the position relative to the centre of the circle in xy-coordinates can be described in terms of the angle or indeed ω and t.
- x = r cos(θ) = r cos(ωt)
- y = r sin(θ) = r sin(ωt)