Analog Vector Clock

A simple analog clock may be simulated using just three Desmos Geometry Tool (DGT) elements and a pair of user‑defined polar vector functions. Polar vector notation is commonly used to solve a wide variety of real‑world scientific and engineering problems.

Vector Clock

👉 At the beginning of the DGT file, an input slider is scaled so that the minute hand completes 12 full rotations. Click the play button to animate the system.

Input Slider

👉 Unit circle is defined using the origin and the point (0, 1) as the reference definition points.

Unit Circle

👉 Minutes vector starts at the origin, with a magnitude of 0.95.  Its direction is defined opposite the angular displacement input, enforcing clockwise rotation.

Minutes Vector

👉 Hours vector starts at the origin with a magnitude of 0.65. Its direction is defined opposite the angular displacement input, enforcing clockwise rotation, and the minutes‑vector angular displacement is scaled by 1/12 to represent the hourly rate.

Hours Vector

👉 Required functions: two function definitions from the VTools Functions library are required for this solution—Vpolar and Vp2. Use the preceding link for documentation to help implement these functions in your own Desmos Geometry Tool solutions.

👉 Compatibility note: these vector functions do NOT work in the Desmos Graphing Calculator (DGC).

VTools  Functions

FBD Nomenclature

Disclaimer: WORK IN PROGRESS

This table will be updated regularly in the coming months as I work through problems with students on homework and test preparation. Desmos solutions posted on this blog will aim to use this nomenclature consistently.

Suggested Desmos variables nomenclature for AP Physics 'Free Body Diagrams' (FBDs), respecting Desmos calculator's built-in variable-naming limitations.  

For example:

• Desmos does NOT allow subscripted or superscripted Greek letters or punctuation characters
• All sub- and superscripts must be either upper- or lower-case letters, or integers
• Desmos imposes limitations on θ all by itself, requiring a subscript for general usage