Home / Topics / Momentum & Collisions
Billiard ball collisions
Intermediate
Equal-mass elastic collisions split paths at 90°.
In an off-centre elastic collision of equal masses with one at rest, the two balls leave at right angles to each other. The impact line determines the target's direction.
Break shots in pool.
This needs equal masses and elastic, frictionless contact.
In more detail
Billiard collisions approximate elastic collisions between equal-mass balls. The cue ball and target ball move at right angles after a glancing collision, which is a well-known result.
Real-world uses
- Players aim using the right-angle rule for equal-mass collisions.
- Physics teachers use billiards to illustrate momentum conservation.
- In a perfectly elastic head-on or glancing collision between equal balls, the cue ball and the struck ball move at right angles.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
Why at right angles?
For equal masses in an elastic collision, the velocities after a glancing blow are perpendicular.
Is friction important in billiards?
Yes. Spin and friction affect the outcome, which the simple model ignores.
Why do the balls move at right angles?
For equal masses in an elastic collision, the final velocities are perpendicular when the target is struck off-centre.
Related topics in Momentum & Collisions
Energy lost in inelastic collision · Reduced mass · Collisions in two dimensions · Ballistic pendulum · Bouncing ball · Centre of mass