Circular motion as superposition of motions along x and y axes
Circular motion is a typical motion in two dimensions. It can be seen as two independent motions along x and y axes, similar to projectile motion.
In Fig.1 explanation of this statement is given.
Radius R is rotating with angular frequency ω about the virtual axis perpendicular to the plane of drawing, passing trough the point O. The angle α is a function of time defined as
(1)
See the previous point (Uniform circular motion) for definitions of angular frequency w, period T, and frequency f. The end of the arrow moves on a circle of radius R.
At any given instant of time position of the end of the arrow is given by coordinates
x(t) = Rcosα (2)
y(t) = Rsinα (3)
The circular motion can be seen as a simultaneous motions of an object along the x and y axes, with positions given by Eqs.2 and 3, with time dependence resulting from Eq.1.
Later on, when studying dynamics (motion resulting from acting forces) we will learn that individual motion along the x or y axis according to Eq. 2 or Eq.3 is an example of harmonic motion.