Assume a particle with mass m has angular velocity ω about an axis. The particles speed is v = ωr. The particle has angular momentum. We define the angular momentum L of the particle about the axis as as L = mr2ω, where r is the perpendicular distance of the particle from the axis of rotation. L is a vector. Its direction is the direction of ω. If we increase the perpendicular distance of the particle from the axis of rotation, or if we increase its rate of rotation, we increase the magnitude of its angular momentum.
For an object consisting of many particles mi (i = 1, 2, 3, ...), the total angular momentum about an axis is the vector sum of the angular momenta of all the particles about the axis.
L = ΣiLi, Li = mri2ω. (The symbol Σi denotes the sum over all the particles.)
The SI unit for angular momentum is kg m2/s
In interactions between isolated objects angular momentum is always conserved.
In the video clip shown below the total angular momentum of the system points upward. The person is stopping a spinning wheel and start to spin on the stool.
Some of the first few frames:
The magnitudes of the angular momenta of the wheel and of the person change at the same rate, but their sum remains constant.