Recording-2025-03-04T15:08:31.767Z.m4a

Angular Momentum

• Angular Momentum: A physical quantity that represents the rotational inertia and rotational velocity of an object. It is a vector quantity, which means it has both magnitude and direction.

Definition

• The angular momentum (L) of an object is defined as the product of its moment of inertia (I) and its angular velocity (ω).

  • Formula: L = I × ω

Moment of Inertia

• Moment of Inertia: A measure of an object's resistance to changes in its rotation. It depends on the mass distribution of the object relative to the axis of rotation.

  • For point masses: I = m × r², where m is the mass and r is the distance from the axis of rotation.

Angular Velocity

• Angular Velocity: The rate of change of angular displacement with respect to time.

  • Measured in radians per second (rad/s).

Conservation of Angular Momentum

• Conservation Law: The total angular momentum of a closed system remains constant if no external torques act on it.

  • Implication: If one aspect of the system changes (e.g., moment of inertia decreases), another aspect must change (e.g., angular velocity increases) to conserve total angular momentum.

Application

• Used in various fields, including physics, engineering, and even sports.

• Example: An ice skater spins faster by pulling their arms in, reducing moment of inertia.