A Classical Approach of Newtonian Mechanics

7 CIRCULAR MOTION

7 Circular motion

7.1 Introduction

Up to now, we have basically only considered rectilinear motion: i.e., motion in

a straight-line. Let us now broaden our approach so as to take into account the

most important type of non-rectilinear motion: namely, circular motion.

7.2 Uniform circular motion

Suppose that an object executes a circular orbit of radius r with uniform tan-

gential speed v. The instantaneous position of the object is most conveniently

specified in terms of an angle θ. See Fig. 57. For instance, we could decide that
θ = 0 ◦ corresponds to the object’s location at t = 0 , in which case we would write

θ(t) = ω t, (7.1)

where ω is termed the angular velocity of the object. For a uniformly rotating
object, the angular velocity is simply the angle through which the object turns in
one second.

t = 0

t = t

v

Figure 57: Circular motion.

Consider the motion of the object in the time interval between t = 0 and t = t.
In this interval, the object rotates through an angle θ, and traces out a circular

arc of length s. See Fig. 57. It is fairly obvious that the arc length s is directly

v

s

r (t)^

r