Angular momentum is the moment of linear momentum. Areal velocity of a particle is half the ratio of angular momentum and mass of particle.
External torque acting on a system of particles is zero, the angular momentum of the system remains constant. This statement is called the principle of conservation formula of angular momentum.Conservation of Angular MomentumThe law states that “If the external torque acting on the body is zero, the angular momentum formula of the body remains constant”Proof: If a body rotates with constant acceleration α under the action of an external torque , then according to Newton’s second law of rotator motion.Where L = angular momentum of the body
This is the law of conservation of angular momentum.Remark:This law is analogous to the law of conservation of linear momentum. According to which if external force acting on a body is zero, the linear momentum of the body remains constant.Conservation of angular momentum formula under central forceThe torqueThe torque vanishes when the force is parallel. It acts towards or away from the centre O. such a force is called the central force.
That is the central force is one which depends only on distance® of particle from a fixed centre O and is directed towards.In other words a force F is said to be central if it is parallel to r. so for a central force,Thus, if the force acting on a particle is central, the angular momentum formula of the particle remains conserved.
The well known examples of central forces are the gravitational force between two point masses and the coulomb’s force between two point charges.Example of conservation of angular momentumConservation of Angular momentum of planet about the sun:Each planet revolves around the sun in elliptical orbit with sun at one focus of the ellipse. The gravitational force of sun acts on the planet. As gravitational force is central force, formula for the angle between force and position vector is 180⁰.
Angular momentum of electron about the nucleus:According to modern atom model, atom consists of positively charged nucleus at the centre and electrons circulate around it in definite circular or elliptical orbits. The electron coulomb’s attractive force of nucleus. The coulomb’s force is central, angle between F and r is 180⁰, so torqueHence angular momentum of electron about the nucleus is constant.