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In geometry you learned that the area of a circle of radius $$r$$ is $$πr^ 2$$ . We will now learn how to find the area of a sector of a circle. A sector is the region bounded by a central angle and its intercepted arc, such as the shaded region in Figure 4.3.1.
So suppose that an object moves along a circle of radius r, traveling a distance s over a period of time t, as in Figure 4.4.1. Then it makes sense to define the (average) linear speed ν of the object as: $$v=\frac{s}{t}$$. Let θ be the angle swept out by the object in that period of time. Then we define the (average) angular speed ω of the object as: $$ω = \frac{θ}{ t}$$.
Thumbnail: Angle $$θ$$ and intercepted arc $$\overparen{AB}$$ on circle of circumference $$C = 2πr$$.