A Classical Approach of Newtonian Mechanics

11 OSCILLATORY MOTION 11.6 Uniform circular motion

y

x

Figure 99: Uniform circular motion.

Since the object is executing uniform circular motion, we expect the angle θ to
increase linearly with time. In other words, we can write

θ = ω t, (11.34)

where ω is the angular rotation frequency (i.e., the number of radians through

which the object rotates per second). Here, it is assumed that θ = 0 at t = 0, for
the sake of convenience.

From simple trigonometry, the x- and y-coordinates of the object can be writ-
ten

x = a cos θ, (11.35)

y = a sin θ, (11.36)

respectively. Hence, combining the previous equations, we obtain

x = a cos(ω t), (11.37)

y = a cos(ω t − π/2). (11.38)

Here, use has been made of the trigonometric identity sin θ = cos(θ − π/2). A
comparison of the above two equations with the standard equation of simple har-
monic motion, Eq. (11.3), reveals that our object is executing simple harmonic



a a^ sin



a cos (^) 