Ball in a Square Hole — Elastic Wrap Simulation

Physics

Enable square rotation

moment of inertia I—

ω (rad/s)—

angle (°)—

I = m (a² + b²) / 6 for a uniform square frame (outer a, hole b). With rotation off, I is treated as infinite (ω locked at 0).

Time scale

speed1.00×

Display

Velocity vectors Center of mass Ball trail Grid & wrap seam

Live state (conserved)

ball speed—

ball v(x,y)—

square speed—

square v(x,y)—

|momentum| now / init— / —

kinetic energy now / init— / —

angular mom. now / init— / —

COM drift speed—

Legend

square frame (mass 1)

ball Ø10 (mass 1)

system center of mass

Restitution e = 1 (perfectly elastic, no loss). Impulse includes torque through the contact lever arm when rotation is enabled. Tangential motion is untouched → no friction.

Linear momentum and total KE (translational + rotational) stay constant. On a free torus there is no external torque about the COM, so total angular momentum is also conserved.

Wrap is handled with a wrap-aware relative coordinate, so collisions stay correct when the square crosses the 1024 seam.