Conservation of angular momentum derivation

Conserved physical quantity; rotational analogue of linear momentum

Angular momentum
This gyroscope remains upright while spinning owing to the conservation of its angular momentum.
Common symbols	L
In SI base units	kg⋅m2⋅s−1
Conserved?	yes
Derivations from other quantities	L = Iω = r × p
Dimension

Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum.

It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved.

Conservation of angular momentum formula

Bicycles and motorcycles, flying discs,^[1]rifled bullets, and gyroscopes owe their useful properties to conservation of angular momentum. Conservation of angular momentum is also why hurricanes^[2] form spirals and neutron stars have high rotational rates.

In general, conservation limits the possible motion of a system, but it does not uniquely d

angular momentum will be conserved when

angular momentum of system of particle is conserved when