Example 3: Angular Velocity

A particle travels around a vertical circle of radius r₀ with constant angular velocity ω = dθ/dt, beginning with θ = 0 at time t = 0. If the sun is directly overhead, find the position, velocity, and acceleration of the shadow.

Let us center the circle at the origin in the (x, y) plane (Figure 7.2.5). Then x = r₀ cos θ, y = r₀ sin θ.

Figure 7.2.5