## Conservation of Angular Momentum – Class 11 | Chapter – 7 | Physics Short Notes Series PDF for NEET & JEE

Conservation of Angular Momentum: The conservation of angular momentum is a fundamental principle in physics that states that the total angular momentum of a system remains constant if no external torque acts on the system. In other words, angular momentum is conserved in the absence of external torques.

Angular momentum is a vector quantity, and its direction is perpendicular to both the object’s axis of rotation and the direction of its velocity. The magnitude of the angular momentum depends on the object’s mass, velocity, and distance from the axis of rotation.

## Conservation of Angular Momentum

The conservation of angular momentum can be described mathematically by the equation:

Linitial = Lfinal

Where,

• Linitial is the initial angular momentum of the system
• Lfinal is the final angular momentum of the system

For example, consider a figure skater spinning on the ice with her arms outstretched. When she brings her arms in towards her body, her moment of inertia decreases, but her angular velocity increases, resulting in an increase in her angular momentum. However, the total angular momentum of the system (the figure skater and the ice) remains constant because no external torque is acting on the system.

## Importance of Conservation of Angular Momentum

The principle of conservation of angular momentum is of great importance in physics, and it has numerous applications in various fields of science and engineering. Here are some of the key reasons why conservation of angular momentum is important:

• Understanding the motion of celestial bodies: It is used to explain the behavior of planets, stars, and galaxies. For example, the conservation of angular momentum explains why planets orbit the sun in nearly circular paths and why stars rotate at a constant rate.
• Designing machines and vehicles: It is used to design machines and vehicles that require stable and efficient rotation, such as turbines, gyroscopes, and spacecraft. Engineers use the principle of conservation of angular momentum to optimize the design of these systems and ensure that they operate reliably.
• Understanding particle physics: It is used to understand the behavior of subatomic particles, such as electrons, protons, and neutrons. It explains why certain particles have a spin and how they interact with electromagnetic fields.
• Solving problems in mechanics: It is an essential tool in solving problems in mechanics. It enables physicists to analyze the motion of rotating systems, such as a spinning top or a rotating planet, and predict their behavior under various conditions.
• Explaining astronomical phenomena: It is used to explain a wide range of astronomical phenomena, such as the formation of accretion disks around black holes, the spin of neutron stars, and the rotation of galaxies.

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