Law of Conservation of Angular Momentum
In physics, the linear momentum, p = mv, has a rotational analog. It is called angular momentum (rarely, moment of momentum
or rotational momentum
), L, and for an object rotating about a fixed axis with angular velocity ω, it is defined as:
L = Iω
It is an important quantity in physics because it is a conserved quantity:
The angular momentum of an isolated system remains constant in both magnitude and direction.
When there is zero net torque acting on an object, and the object is rotating about a fixed axis or about an axis through its center of mass whose direction doesn’t change, we can write:
I1ω1 = I2ω2 = constant
Like conservation of energy and of linear momentum, this principle is a universal conservation law, valid at all scales from atomic and nuclear systems to the motions of galaxies. The angular momentum is a vector quantity and therefore it can be generalized as:
The vector sum of the angular momenta of the parts of an isolated system is constant.
This puts a strong constraint on the types of rotational motions which can occur in an isolated system. If one part of the system is given an angular momentum in a given direction, then some other part or parts of the system must simultaneously be given exactly the same angular momentum in the opposite direction.
The law of conservation of angular momentum explains the angular acceleration of an ice skater as she brings her arms and legs closer to the vertical axis of rotation. By bringing part of the mass of her body closer to the axis she decreases her body’s moment of inertia. Because angular momentum is the product of moment of inertia (I) and angular velocity (ω), and the angular momentum remains constant according to this law, the angular velocity of the skater must increase.
I1ω1 = I2ω2