Conical Pendulum Meets Uniform Circular Motion: Parameterized Vector Geometry

This example visualizes a conical pendulum’s motion under geometric constraints and links it to the trajectory and direction structure of uniform circular motion (UCM). The key ideas include vector-based representation of motion, circle geometry, using angle measures to relate direction changes, and a parameter/animation-driven interpretation of position over time. Construction emphasizes: Circle and Point to create the circular path and the moving mass, Line and Segment to form geometric connections used for direction/constraint visualization, Vector and Angle to compute and display direction relationships (e.g., velocity/displacement-related vectors), OrthogonalPlane plus Intersect to build and use relevant orthogonal projections/constraint intersections, and Cone to represent the conical surface of the pendulum’s spatial geometry. Supporting commands like If and animation controls (e.g., anima/reset/start) allow interactive parameter variation and dynamic updating. Suitable for upper secondary to introductory university modeling and visualization of circular motion and vector geometry.