Some Terminology

Some Terminology

a) Rigid body: A rigid body is defined as a solid body in which the particles are compactly arranged so that the inter-particle distance is small and fixed and is not disturbed by any external forces applied.

b) Angular Momentum: The angular momentum of a particle moving about a fixed axis is the moment of its momentum about the axis. It is simply the product of linear momentum and the perpendicular distance between it and the axis of rotation.Mathematically, \begin{align*}\overrightarrow{J}=\overrightarrow{r}\times \overrightarrow{P}\end{align*}Where \(\overrightarrow{P}\)=m\(\overrightarrow{v}\) is linear momentum.

c) Angular impulse: The angular impulse is defined as the change of angular momentum. i.e. angular momentum is\begin{align*}I\omega =\int_{0}^{t}\tau\times dt\end{align*}Where I is the moment of inertia=mr².

d) Torque: The torque acting on a body is defined as the moment of the force about the axis of rotation. i.e.\begin{align*}\overrightarrow{\tau}=\overrightarrow{r}\times \overrightarrow{F}\end{align*} Where \(\overrightarrow{F}\) is the applied force and \(\overrightarrow{r}\) is the perpendicular distance between\(\overrightarrow{F}\) and the axis of the rotation.

e) The radius of gyration: The distance from te axis at which if its entire mass (M) be supposed to be concentrated at its centre, its moment of inertia about the given axis would be the same as with its actual distribution of mass. Its is denoted by K and it is given by\begin{align*}K=\sqrt{\frac{(r_{1}^{2}+r_{2}^{2}+r_{3}^{2}....r_{n}^{2})}{n}}\end{align*}where, n= no. of particles in a body.

References:

Adhikari, Pitri Bhakta. A Textbook of Physics Volume-I. Kathmandu: Sukunda Pustak Bhawan, 2015.

Feynman, Richard P. The Feynman Lectures on Physics Volume 1. Noida: Dorling Kindersley (India) Pvt. Ltd., 2014.

Mathur, D S. Mechanics. New Delhi: S. Chand & Company Pvt. Ltd., 2015.

Young, Hugh D, Roger A Freedman and A Lewis Ford. University Physics. Noida: Dorling Kindersley (India) Pvt. Ltd., 2014