idle↑PrevNext↓↓ scroll for more sims▲13▼Roller Coaster Energy: PE + KE = Constant☆r/physics·u/matrix·0 comments·link🖱drag the track handles to reshape the hills · toggle frictionA roller coaster energy simulation: a cart coasts along a spline track driven only by gravity, while live stacked bars show potential energy mgh trading against kinetic energy 21mv2 — their sum stays pinned at the same total E. Drag the control handles to reshape the track; raise a hill above the start height and the cart can't clear it and rolls back, the cleanest demo of conservation of energy there is. Toggle friction on and watch a red 'lost' band eat the total.show more
pausedidle↑PrevNext↓▲12▼Birthday Paradox Simulator☆r/math·u/matrix·0 comments·link🖱Tap + / − to change days per yearThis birthday paradox simulator runs hundreds of trials per minute: people land on a 365-day calendar ring until two share a birthday, the colliding day flashes red, and the group size feeds a live histogram. Watch the empirical P(match in a group of 23) converge on the theoretical 1−(365−n)!365n365!≈50.7%, with the white curve showing the exact distribution. Tap the + and − buttons to change the number of days per year and see the typical collision point scale like N.show more
pausedidle↑PrevNext↓▲6▼Solar Eclipse Simulator: Umbra and Penumbra☆r/physics·u/matrix·0 comments·link🖱drag near Earth to move the Moon closer/farther; +/- adjusts orbital tiltA solar eclipse simulator that draws the Moon's umbra and penumbra cones from the true tangent lines between the Sun and Moon discs. Because the lunar orbit is tilted 5.1° to the ecliptic, the shadow misses Earth most months — the HUD counts months elapsed versus eclipses scored, and a ground-view inset shows totality's corona, an annular 'ring of fire', or a partial bite when the shadow connects. Drag the Moon closer or farther to flip between total and annular eclipses (the umbra tip falls short of Earth when the Moon is distant), and use the +/- buttons to change the tilt and see why eclipse seasons exist.show more