ONE COLLISION. TWO DIRECTIONS.
Meet at an angle.
Launch either particle, shift the aim and follow how momentum is shared in two dimensions.
The collision
Ready to launch● A · small particle● B · large particleArrows show velocity, with a shared scale
Top-down view on a frictionless surface. Before launch, drag the moving particle sideways to adjust the aim; the offset slider also works with a keyboard. The camera stays fixed as you change the setup. The full experiment runs inside the same arena.
Momentum: before and after
Calculated collision outcomesMomentum is conserved separately along the fixed x and y axes. The stationary particle initially has zero momentum.
Along y
| Particle | Before: pₓ | Before: pᵧ | After: pₓ | After: pᵧ |
|---|
Where did the energy go?
Why the paths change
Conserve both components
There is no external horizontal impulse. The particles exert equal and opposite impulses on each other, so one particle’s momentum change is the negative of the other’s in both directions.
Contact sets the deflection
The collision impulse acts along the line joining the centres at contact. With smooth particles there is no tangential impulse. Moving the aim changes this contact direction and the outgoing velocities.
For e = 1, kinetic energy is conserved. For e < 1, some becomes internal energy, deformation or sound; total energy is still conserved.
e = 0 means no relative separation speed along the contact normal. In an off-centre collision the particles can still slide past each other—they are not glued together.
Model and units
Ideal smooth, non-rotating circular particles with fixed radii 0.32 m and 0.48 m. Mass is independent of drawn size. Motion and impact time are evaluated analytically; collision impulses are instantaneous. The coefficient of restitution applies to the relative normal velocity. No friction, spin, gravity in the viewing plane, walls or subsequent wall collisions. Kinetic energy here includes translation only. Velocity arrows share a scale; tiny components may be visually short. Values are rounded for display.
Reference: Applied Mechanics — impulse, momentum and oblique impact.
Explore two-dimensional collisions
Launch either of two smooth particles on a frictionless surface. Change their masses, launch speed, direction, aim offset and coefficient of restitution. The permitted aim range guarantees contact. A fixed camera shows the particles and their velocity vectors before and after impact.
Pause, scrub through time or jump immediately before and after the collision. Compare the momentum components of both particles and verify that total momentum is conserved separately along x and y. Inspect the kinetic energy transferred between particles or to other forms in an inelastic collision. This interactive resource supports IB, A Level and AP Physics learning.