Question

What is angular momentum?

Answer 1

The angular momentum of a particle of mass m with respect to a chosen origin is given by

L = mvr sin θ

or more formally by the vector product

L = r x p

The direction is given by the right hand rule which would give L the direction out of the diagram. For an orbit, angular momentum is conserved, and this leads to one of Kepler's laws. For a circular orbit, L becomes

L = mvr

The angular momentum of a rigid object is defined as the product of the moment of inertia and the angular velocity. It is analogous to linear momentum and is subject to the fundamental constraints of the conservation of angular momentum principle if there is no external torque on the object. Angular momentum is a vector quantity. It is derivable from the expression for the angular momentum of a particle

L = I

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 m_i (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 = Σ_iL_i,  L_i = mr_i²ω. (The symbol  Σ_i denotes the sum over all the particles.)

The SI unit for angular momentum is kg m²/s

Angular momentum and linear momentum are examples of the parallels between linear and rotational motion. They have the same form and are subject to the fundamental constraints of conservation laws, the conservation of momentum and the conservation of angular momentum .