To determine if a point lies on an arc when moving counterclockwise (CCW) from one point to another on a circle, follow these steps:

1. Understand Angle Measurement: Angles increase in the CCW direction on a unit circle. Starting at 0 radians (east), moving CCW increases angles towards π/2 (north), π (west), 3π/2 (south), and then back to 0.

2. Identify Start and End Points: Let’s denote α as the starting angle and β as the ending angle of the arc.

3. Check Angle Relationships:

   • If α < β: The arc spans from α to β without wrapping around, so any θ between α and β (α ≤ θ ≤ β) lies on the arc.
   • If α > β: The arc wraps around the circle, meaning it goes from α to 2π and then continues from 0 to β. Therefore, θ lies on the arc if it is either ≥ α or ≤ β.

4. Apply Conditions:

   • For α < β: θ ∈ [α, β]
   • For α > β: θ ∈ [α, 2π] ∪ [0, β]

5. Example Application:

   • Let α = 3π/2 (~4.712) and β = π/2 (~1.5708).
   • Since α > β, the arc spans from 3π/2 to 2π and then from 0 to π/2.
   • To check if θ = π (~3.14) is on this arc:
     • Is π ≥ 3π/2? No (3.14 < 4.712).
     • Is π ≤ π/2? No (3.14 > 1.5708).
   • Therefore, θ = π does not lie on the CCW arc from α to β.

Final Answer: The point θ = π is not on the CCW arc from 3π/2 to π/2 because it does not fall within either [3π/2, 2π] or [0, π/2].

\boxed{\text{No}}