Physics Simulation & Angular Deceleration Mathematics
Realistic spinning wheel animations rely on rotational dynamics governed by Newton's Second Law of Rotational Motion: $\tau = I \alpha$, where $\tau$ represents the net frictional torque, $I$ is the moment of inertia, and $\alpha$ is angular acceleration. Rather than applying a linear velocity decrease that feels jarring and unnatural, our physics engine models viscous exponential damping:
Here, $\omega_0$ is the initial angular velocity imparted by the spin impulse, and $\mu$ is the rotational friction coefficient. This creates the authentic physical suspense of rapid initial rotation followed by an asymptotic, suspenseful crawl toward the final resting slice.
Uniform Angular Partitioning Algorithm
For any list containing $N$ valid entries, the circle is partitioned into $N$ equal circular sectors of angle $\theta$:
Because the top indicator needle sits at $3\pi / 2$ (270 degrees or straight top), the winner index is resolved mathematically by evaluating the inverted rotation angle modulo $2\pi$:
Classroom Gamification & Fair Raffle Principles
| Governance Standard | Compliance Mechanism | Educational / Raffle Benefit |
|---|---|---|
| Equal Probability | Exact $\theta = 360^\circ / N$ geometric slicing | Zero visual bias or unequal segment weightings |
| Cryptographic Entropy | crypto.getRandomValues() impulse seed | Eliminates predictable PRNG cycle exploits |
| Zero Roster Leakage | Client-side heap memory confinement | FERPA & COPPA privacy compliance for students |