A point mass m in the body will execute a circular motion about the fixed axis.

Angular Momentum and Angular Velocity

Let us consider a rigid body rotating about a fixed axis. A point mass m in the body will execute a circular motion about the fixed axis as shown in Figure 5.12.

The point mass m is at a distance r from the axis of rotation. Its linear momentum at any instant is tangential to the circular path. Then the angular momentum is perpendicular to and . Hence, it is directed along the axis of rotation. The angle θ between and in this case is 90o. The magnitude of the angular momentum L could be written as,

L = rmv sin90o = rmv

where, v is the linear velocity. The relation between linear velocity v and angular velocity ω in a circular motion is, v = r ω. Hence,

The directions of L and ω are along the axis of rotation. The above expression can be written in the vector notation as,

As discussed earlier, the term mr2 in equations 5.22 and 5.23 is called moment of inertia (I) of the point mass. A rigid body is made up of many such point masses. Hence, the moment of inertia of a rigid body is the sum of moments of inertia of all such individual point masses that constitute the body ( I = ∑mi ri 2 ). Hence, the angular momentum of the rigid body can be written as,

The study about moment of inertia (I) is reserved for Section 5.4.

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

11th Physics : Motion of System of Particles and Rigid Bodies : Angular Momentum and Angular Velocity |

**Related Topics **

Privacy Policy, Terms and Conditions, DMCA Policy and Compliant

Copyright © 2018-2023 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.