Systems Of Particles And Rotational Motion

This section introduces the concepts of systems of particles and rotational motion, focusing on the motion of extended bodies and the significance of the center of mass.

Introduction

This section introduces the concept of extended bodies and their motion, emphasizing the importance of the center of mass and the distinction between translational and rotational motion.

What Kind Of Motion Can A Rigid Body Have?

This section discusses the types of motion that a rigid body can exhibit, including pure translational motion and rotation about a fixed axis.

Centre Of Mass

The section explores the concept of the center of mass for a system of particles, including its definition and significance in understanding motion.

Motion Of Centre Of Mass

This section discusses the motion of the center of mass for systems of particles, emphasizing how it simplifies the analysis of these systems.

Linear Momentum Of A System Of Particles

This section discusses the concept of linear momentum for a system of particles, establishing its relation to the motion of the system's center of mass and the implications of external forces.

Vector Product Of Two Vectors

This section introduces the vector product, also known as the cross product, which yields a vector from two input vectors, highlighting its significance in physics, particularly in rotational motion.

Angular Velocity And Its Relation With Linear Velocity

This section discusses the concept of angular velocity and its relationship with linear velocity in the context of rotational motion.

Angular Acceleration

This section introduces the concept of angular acceleration as the rate of change of angular velocity in rotational motion.

Torque And Angular Momentum

This section introduces torque and angular momentum, highlighting their significance in rotational motion and the mathematical relationships involved.

Moment Of Force (Torque)

This section covers the concept of torque and its significance in rotational motion, explaining how torque relates to the moment of force and dynamics of rigid bodies.

Angular Momentum Of A Particle

This section covers the definition of angular momentum for a particle and its applications, emphasizing its role as the rotational analogue of linear momentum.

Equilibrium Of A Rigid Body

This section discusses the conditions required for a rigid body to be in equilibrium, considering both translational and rotational forces acting upon it.

Principle Of Moments

The Principle of Moments states that for an object to be in equilibrium, the sum of clockwise moments around a pivot must be equal to the sum of counterclockwise moments.

Centre Of Gravity

The section covers the concept of the centre of gravity (CG) and its significance in determining the balance of objects.

Moment Of Inertia

This section introduces the concept of moment of inertia, the rotational analogue of mass, and explores its applications in calculating the kinetic energy of rotating bodies.

Kinematics Of Rotational Motion About A Fixed Axis

This section delves into the kinematics of rotational motion around a fixed axis, drawing parallels with linear motion concepts.

Dynamics Of Rotational Motion About A Fixed Axis

This section discusses the dynamics of rotational motion about a fixed axis, establishing key parallels between linear and rotational motion.

Angular Momentum In Case Of Rotation About A Fixed Axis

This section discusses angular momentum in the context of rotational motion about a fixed axis, emphasizing its conservation and relation to torque.

Conservation Of Angular Momentum

This section focuses on the principle of conservation of angular momentum, particularly during rotation about a fixed axis, explaining that when the total external torque is zero, the angular momentum remains constant.

Summary

The section summarizes the fundamental concepts of motion in rigid bodies, focusing on rotational and translational motion.

Points To Ponder

This section discusses the motion of the center of mass and its significance in understanding systems of particles and rigid bodies.

Exercise

This section contains various exercises designed to reinforce knowledge about systems of particles and rotational motion.