In this topic we deal with rotational and translation motion of the rigid bodies. We uncover some of the important topics of physics such as torque, angular momentum, conservation of angular momentum and moment of inertia.

Importance

Rotational Mechanics is in the syllabus for both JEE mains and JEE Advanced. In the last 5 years nearly 7 questions came in JEE mains. Counting the online exams as separate exams, we see that approximately 1 question comes from this topic in JEE mains, though not every year. Similarly, in JEE Advanced, 8 questions were asked in the last 5 years, so we can expect 1 or 2 questions may come from Rotational mechanics. Rotational mechanics is more important if you are focussing on JEE Advanced.

Introduction

Here is a nice introductory video about Rotatory motion and the newton's laws in rotatory motion.

Torque

Torque is nothing but a vector product of perpendicular distance and force. Torque is denoted by a greek letter tau.

tau=rxxF

Moment of Inertia

Moment of inertia is the mass property of a rigid body that determines the torque needed for a desired angular acceleration about an axis of rotation. Moment of inertia depends on the shape of the body and may be different around different axes of rotation.

You can go click on the diagrams in the Common moments of Interia diagram for complete derivations of M.O.I, in the above linked page.

Angular momentum

Angular momentum is the product of moment of inertial and angular velocity.

L=Iomega=rxxp

where p is momentum and r is perpendicular distance.

Conservation of Angular Momentum

The law of conservation of angular momentum states that " When no external torque acts on an object or a closed system of objects, no change of angular momentum can occur "

(dL)/(dt)=0

Rolling Motion

Rolling motion is the combination of rotaional as well as translational motion. There are two types of rolling motion.

1) Rolling without slipping (Pure Rotational motion)

2) Rolling with slipping.