Is this good for educators?

Yes — this version of "Rotational Dynamics for a projectile from a cannon" is framed for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs.

Do I need to install anything?

No. It runs in any modern browser, free, with no account required.

For Educators · Rotational Dynamics

Rotational Dynamics for a projectile from a cannon

Built for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs. Simulate a projectile from a cannon live below — adjust the inputs and watch it respond, right in your browser.

Collisions

open full solver →

Elastic CollisionsLive

momentum & energy conservation

Controls

Speed1×

Presets

Balls collide with impulse-based physics. At restitution 1, kinetic energy is conserved; below 1, collisions are inelastic and energy drains away.

Balls

Restitution

▶ Run in Python

Data Inspector

Balls12

Total KE0.00e+0

Collisionselastic

Governing equation

j = \frac{- ( 1 + e ) ( v _{b} - v _{a} ) \cdot n ^}{1/ m _{a} + 1/ m _{b}}, e = 1.00

Reading this result: With restitution 1 every bounce is perfectly elastic, so the total kinetic energy of all 12 balls stays constant forever — a 2D model of an ideal gas.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

↓

Double Pendulum

open full solver →

Double Pendulum StudioLive

chaotic dynamics · RK4

Controls

Speed1×

Tiny changes in the start explode into totally different motion — deterministic chaos. Drag either bob to set a new starting position; it pauses playback automatically.

Presets

Lower bob mass

Gravity g

▶ Run in Python

Data Inspector

IntegratorRK4

SystemChaotic

DOF2

Lower bob mass10

Gravity g9.8

Governing equation

\ddot{θ}_{1} \ddot{θ}_{2} = \frac{- g ( 2 m _{1} + m _{2} ) sin θ _{1} - m _{2} g sin ( θ _{1} - 2 θ _{2} ) - 2 m _{2} sin ( θ _{1} - θ _{2} ) ( θ ˙ _{2}^{2} L _{2} + θ ˙ _{1}^{2} L _{1} cos ( θ _{1} - θ _{2} ) )}{L _{1} ( 2 m _{1} + m _{2} - m _{2} cos ( 2 θ _{1} - 2 θ _{2} ) )} = \frac{2 sin ( θ _{1} - θ _{2} ) ( θ ˙ _{1}^{2} L _{1} ( m _{1} + m _{2} ) + g ( m _{1} + m _{2} ) cos θ _{1} + θ ˙ _{2}^{2} L _{2} m _{2} cos ( θ _{1} - θ _{2} ) )}{L _{2} ( 2 m _{1} + m _{2} - m _{2} cos ( 2 θ _{1} - 2 θ _{2} ) )} m_{1} = 10, m_{2} = 10, L_{1} = L_{2} = 1.2, g = 9.8

Reading this result: Starting both arms at 90° (π/2) with lower-bob mass 10 and g 9.8 puts the pendulum firmly in its chaotic regime. Unlike a small-angle swing, which would be near-periodic, here trajectories that differ by 0.02 rad diverge exponentially — a positive Lyapunov exponent.

Runs locally in your browser — free forever. Scale to the cloud when reality gets heavy.

or unlock everything with Pro →

Also for:Students Researchers Engineers Hobbyists & Makers K-12 Students First Responders General version →

More with Rotational Dynamics

Rotational Dynamics for a bouncing ball Rotational Dynamics for a pendulum clock Rotational Dynamics for a car braking Rotational Dynamics for a roller-coaster loop Rotational Dynamics for a satellite orbit Rotational Dynamics for a mass on a spring Rotational Dynamics for a skydiver's free fall Rotational Dynamics for a two-cart collision

Frequently asked questions

Is this good for educators?: Yes — this version of "Rotational Dynamics for a projectile from a cannon" is framed for educators teaching it to a class. Drop a live demo into a lecture or assign it as a shareable link — no lab installs.
Do I need to install anything?: No. It runs in any modern browser, free, with no account required.