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Mechanics

7 articles on mechanics: the maths or physics explained, ready-to-teach lesson plans, and how to build each slide in Tracé.

Three trajectories at the same speed: 30° and 60° land together at 35.3 m, 45° goes furthest at 40.8 mphysics · mechanics · high school · explainerWhy 45° Is the Best Launch Angle (and When It Isn’t)The proof that 45° gives the longest throw, why 30° and 60° land in the same place, and why real throws use less: launch height and air resistance.Two balls racing from the same start: the one on a cycloid curve is ahead of the one on a straight rampphysics · mechanics · calculus · explainerThe Brachistochrone: Why the Fastest Path Is a CurveWhy a ball on a cycloid beats one on a straight ramp (3.17 s against 3.76 s for a 20 m drop), the 1696 challenge behind it, and how to animate the race.A free-body diagram of a box with normal force, weight, a push and friction, next to ΣF = ma giving a = 4 m/s²physics · mechanics · high school · lesson planFree-Body Diagrams and Newton’s Second Law: A Lesson PlanHow to teach free-body diagrams step by step, a worked example (30 N push, 10 N friction, 5 kg: a = 4 m/s²), the classic mistakes and check questions.Vectors a = (3, 1) and b = (1, 3) drawn head to tail, with their sum (4, 4) as a dashed arrowphysics · mechanics · high school · lesson planAdding Vectors Head to Tail: A Lesson PlanTeach vector addition: head-to-tail drawings, adding components, the magnitude with Pythagoras, a river-crossing example, common mistakes and checks.A pendulum swinging through a small angle θ, next to T = 2π√(L/g) and T ≈ 2.0 s for L = 1 mphysics · mechanics · high school · lesson planThe Simple Pendulum Period: T = 2π√(L/g) Lesson PlanTeach the simple pendulum period formula T = 2π√(L/g): what changes the period and what does not, the small-angle limit, worked examples and checks.A satellite on a circular orbit around Earth, with its velocity along the orbit and gravity pointing to the centrephysics · mechanics · high school · lesson planCircular Orbits and Gravity: Why Satellites Don’t FallA lesson on circular orbits: gravity as the centripetal force, orbital speed v = √(GM/r), the ISS at 7.7 km/s and 92 minutes, geostationary orbit, and mistakes.A wheel rolling along a line while a point on its rim leaves a yellow cycloid trailteaching tips · animation · mechanicsCustom Maths Animations in a Few Lines, No CodePoints, vectors and curves that move with time: write a rolling wheel or a sliding ladder in six lines of calculator maths, or let the AI write it.