Angular Momentum and Moment of Inertia
Let’s assume that the object is made up of N particles with masses m1, m2,….mN and perpendicular distances r1, r2,….rN from the rotation axis. As the object rotates, all of these particles are in Uniform Circular Motion with the angular speed ω but their linear speeds are,
- v1 = r1ω
- v2 = r2ω
- vN = rNω
Individual velocity directions, v1, v2, and so on, are along the tangents of their respective tracks. The initial particle’s linear momentum is p1 = m1v1 = m1r1ω. It travels in the same direction as v1.
Magnitude of its angular momentum is, L1 = p1r1 = m1r12ω
Similarly, L2 = m2r22ω, L3 = m3r32ω, … LN = mNrN2ω
All of these angular momenta are directed along the axis of rotation for a rigid body with a fixed axis of rotation, which may be determined using the right-hand thumb rule. Their magnitudes may be summed algebraically because they all have the same direction. As a result, the magnitude of the body’s angular momentum is given by,
L = m1r12ω + m2r22ω +….+ mNrN2ω
L = (m1r12 + m2r22 +…+ mNrN2)ω = Iω
Moment of Inertia of body around the given axis of rotation is,
- I = m1r12 + m2r22 +…+ mNrN2
If the moment of inertia I replace mass, the angular momentum statement L = Iω is comparable to the linear momentum expression p = mv, which is its physical significance.
Angular Momentum
Angular Momentum is a kinematic characteristic of a system with one or more point masses. Angular momentum is sometimes called Rotational Momentum or Moment of Momentum, which is the rotational equivalent of linear momentum. It is an important physical quantity as it is conserved for a closed system and follows the Law of Conservation of Angular Momentum. Angular Momentum is equal to the product of the moment of inertia (I), and the angular velocity (ω), of an object in rotational motion. Angular Momentum is a vector quantity. The SI unit of angular momentum is Kg.m2.s-1
Let’s understand more concepts about angular momentum like What is Angular Momentum? Angular Momentum Formula, Unit and Dimensional formula of Angular Momentum, Spin, and Orbital angular momentum, the relation between torque and angular momentum, Law of Conservation of Angular Momentum, FAQs, and Examples of Angular Momentum.
Table of Content
- What is Angular Momentum?
- Angular Momentum Formula
- Angular Momentum of a System of Particles
- Angular Momentum of a Rigid Body
- Right-Hand Thumb Rule
- Angular Momentum and Moment of Inertia