Mechanics playground

Projectile motion, free fall, pendulum/SHM and collisions in one sandbox. Drag the sliders, hit play, and watch the live position and velocity graphs update as the simulation runs.

Lessons

Pick your class, read the steps, then try them right in the sandbox — change one slider at a time and watch the graphs respond.

Class 9 — Equations of motion & free fall

Concept: under gravity alone, a dropped object accelerates uniformly: v = gt and s = ½gt² (starting from rest). The velocity-time graph should be a straight line through the origin — constant acceleration — and the distance-time graph should curve, since distance grows with the square of time.

Switch to Free fall mode.
Set Drop height to 20 m and leave Gravity at 9.8 m/s².
Press ▶ Play and watch the v-t graph — check it really is a straight line.
Reset, then set Gravity to 20 m/s² (a heavier planet) and play again. The object reaches the ground faster — read the new time off the graph and compare it with t = √(2h/g).

Takeaway: the time to fall a fixed height depends only on height and gravity, never on mass — that's why a heavy and light object dropped together land together (no air resistance).

Class 11 — Projectile motion: range and time of flight

Concept: range R = u²sin(2θ)/g and time of flight T = 2u sin(θ)/g. Range is largest at θ = 45°, and two angles that add to 90° (like 30° and 60°) give the same range.

Switch to Projectile motion mode.
Set Launch speed to 20 m/s and Angle to 45°. Press ▶ Play and note the range shown above the stage.
Reset, change the angle to 30°, keep the same speed, and play again. Note the (smaller) range.
Reset, try 60° instead. Compare this range with the 30° one — they should match, confirming the "complementary angles" rule.

Takeaway: maximum range happens at 45°, and range is symmetric around it.

Class 11 — Simple harmonic motion: the pendulum period

Concept: for small swings, a pendulum's period doesn't depend on how far you pull it back (amplitude) — only on its length: T = 2π√(L/g).

Switch to Pendulum & SHM mode.
Set Length L to 1 m and Start angle to 10°. Play and time (or read) one full swing.
Reset, change the Start angle to 25° only — keep the length the same — and play again. The period should barely change, even though the swing is bigger.
Now reset the angle to 10° and instead double the Length to 2 m. Play again — this time the period noticeably increases, matching T ∝ √L.

Takeaway: length changes the period; starting angle (amplitude) barely does, as long as the swing stays small.

Class 11 — Collisions and conservation of momentum

Concept: total momentum (m₁v₁ + m₂v₂) is conserved in every collision, but kinetic energy is only conserved when the collision is elastic (Restitution e = 1).

Switch to Collisions mode.
Set Mass 1 = 2 kg, Mass 2 = 2 kg, v₁ = 5 m/s, v₂ = 0 m/s, and Restitution e = 1.00 (elastic). Play — with equal masses, the moving object should stop and the stationary one takes off at 5 m/s.
Reset, set Restitution e to 0.00 (perfectly inelastic) and play again — the two objects now move off stuck together at a shared, slower velocity.

Takeaway: momentum is conserved either way, but the two masses end up with different final velocities depending on how elastic the collision is.

Position · s–t

Velocity · v–t

What each mode covers

Projectile motion — launch a body at an angle and watch it trace a parabola. Independent horizontal (constant velocity) and vertical (constant acceleration) components, range/height readouts, gravity slider to compare Earth vs Moon vs a made-up planet.

Free fall — drop from a height with no horizontal motion. Confirms v = gt and s = ½gt² directly against the live graphs; toggle two bodies of different mass to see they land together (no air resistance modelled, matching the NCERT idealisation).

Pendulum & SHM — a real (non-small-angle) pendulum, numerically integrated, so a large swing visibly takes longer per cycle than a small one. Compare against the small-angle period formula T = 2π√(L/g) shown live.

Collisions — two masses on a line, elastic (e = 1) through perfectly inelastic (e = 0) via a restitution slider. Momentum is always conserved; kinetic energy readout shows how much is lost as e drops below 1.

Part of Forces — see Learn for the class 9–11 topics these map to, or the constants reference for standard values like g = 9.8 m/s².

Test yourself

Pick Class 9 or Class 11 in the physics quiz to test yourself on motion, Newton's laws, gravitation and work & energy — 10 random questions, with an explanation for every answer.

Take the physics quiz →