Lecture 8 | Classical Mechanics | Angular Momentum Is Conserved Under Central Force

Lecture 8 | Classical Mechanics | Angular Momentum Is Conserved Under Central Force
#classicalmechanics

Welcome to the second part of the lecture on Central Forces. Using the vector equations of velocity and acceleration, we separate the radial part from the angular part. We then consider a particular case of circular motion to show that only the angular part of velocity exists and in the case of acceleration both the radial and angular part contributes to the motion of a particle.

Then we use the angular acceleration part to prove that the angular momentum of a system is conserved under the action of a central force. Under central forces, angular momentum is conserved in classical mechanics. This means that no matter what external forces are applied to a system, its total angular momentum remains constant. This is because any change in linear momentum in a system with a central force is accompanied by an equal and opposite change in angular momentum. This is known as the law of angular momentum conservation.

Angular momentum is a crucial quantity in physics because it is conserved under central forces. It is related to energy conservation and is used to explain many phenomena in a variety of fields. Understanding angular momentum is critical for anyone studying physics and is required for a complete understanding of the laws of motion.

Once we show that the angular momentum is conserved and that the motion occurs on a planar surface only, we will write the equation of motion for the particle that is in motion under the influence of a central force.

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CHAPTERS
00:00 Radial velocity and acceleration, angular velocity and acceleration
02:08 Circular motion
06:15 Expression for angular momentum
12:28 Proof that angular momentum is conserved
18:31 Equation of motion for a particle moving under the influence of a central force
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