Angular momentum of a particle

Intermediate

Position cross momentum.

Key relationL = r×p

L = r × p = mvr sinφ about an origin. A straight-line moving particle has angular momentum about points off its line.

Worked example

1 kg at 3 m/s passing 2 m from the origin: L = 6.

Common mistake

Depends on the origin.

In more detail

For a particle, angular momentum about a point is L = r × p, where r is the position vector and p is the momentum. Its magnitude is r p sin θ.

Satellites in orbit have angular momentum about the planet's centre.
Analysing the motion of a particle around a fixed point.
A particle moving past a pivot has an angular momentum about the pivot, which is useful for analysing orbits.

Does angular momentum depend on the chosen origin?

Yes. It depends on the reference point, so you must specify it.

What is its direction?

Perpendicular to both r and p, following the right-hand rule.

Does a straight-line motion have angular momentum?

Yes, about any point not on the line of motion. Its value depends on the perpendicular distance from the point to the line.