ABSTRACT
Consider a point-like object moving in a circle of radius r (Figure 8.1). As the object moves from point P1 at t1 to point P2 at t2, it sweeps through an arc Δs that subtends an angle Δθ (= θ2 – θ1) at the center, in a time interval Δt = t2 – t1. From geometry
Δs = rΔθ, (8.1)
where Δθ is an angular displacement, measured in radians. To convert an angle expressed in degrees to radians, the following relation may be used:
θ pi θrad
2 rad 360
=
,
(8.2a)
and from radians to degrees, the conversion is
θ
pi θdeg rad
360 2
.=
(8.2b)
Dividing Equation 8.1 by Δt gives the average linear velocity v; that is,
∆ ∆
∆ ∆
s t
r t
=
θ
or
v r .= ω (8.3)
For an object experiencing a constant linear acceleration,
v
v v 2
+ .
