System of Particles

Telegram Channel: https://t.me/+QIV62u7Z3LsxFNeK

CBSE Text Book:

System of particles and rotational motions – web notes

Topic Tree

Topic Tree of “System of Particles and Rotational Motion”

Chapter Overview:

1. Introduction
   • Motion of single particle and extended bodies
   • Definition of rigid bodies
2. Centre of Mass
   • Definition and significance
   • Centre of mass for systems of particles
3. Motion of the Centre of Mass
   • Relation to external forces
   • Applications in translational motion
4. Linear Momentum of a System of Particles
   • Definition
   • Conservation of linear momentum
5. Vector Product of Two Vectors
   • Definition
   • Properties
   • Applications in rotational motion
6. Angular Velocity and Its Relation with Linear Velocity
   • Angular displacement
   • Angular velocity as a vector quantity
7. Torque and Angular Momentum
   • Moment of force (torque)
   • Angular momentum of a particle
   • Conservation of angular momentum
8. Equilibrium of a Rigid Body
   • Conditions for mechanical equilibrium
   • Applications
9. Moment of Inertia
   • Definition
   • Calculation for various shapes
   • Physical significance
10. Theorems of Perpendicular and Parallel Axes
    • Derivation and application
11. Kinematics of Rotational Motion About a Fixed Axis
    • Angular displacement, velocity, and acceleration
12. Dynamics of Rotational Motion About a Fixed Axis
    • Relation between torque and angular acceleration
    • Rotational analogs of Newton’s laws
13. Angular Momentum in Case of Rotation About a Fixed Axis
    • Definition and significance
    • Applications in dynamics
14. Rolling Motion
    • Pure rolling and its conditions
    • Kinetic energy in rolling motion

Terms and Definitions

Term	Definition
System-of-Particles	A collection of particles interacting with each other and potentially subjected to external forces.
Centre-of-Mass	The point at which the total mass of a system of particles can be considered to be concentrated.
Rigid-Body	An ideal body with perfectly fixed shape and size, where the distance between any two points remains constant.
Linear-Momentum	A vector quantity representing the product of mass and velocity of an object (P = mv).
Angular-Velocity	The rate at which an object rotates about a fixed axis (ω = dθ/dt).
Torque	The rotational equivalent of force, representing the moment of force about an axis (τ = r × F).
Angular-Momentum	The rotational analog of linear momentum, defined as L = r × p.
Moment-of-Inertia	A scalar measure of an object’s resistance to rotational motion about an axis (I = Σmᵢrᵢ²).
Rotational-Kinetic-Energy	The energy possessed by a body due to its rotational motion (KE_rot = 0.5 Iω²).
Equilibrium-of-Rigid-Body	A state where the net force and net torque on a rigid body are zero.
Theorem-of-Parallel-Axes	Moment of inertia about a parallel axis is I = I_COM + Md².
Theorem-of-Perpendicular-Axes	For a planar object, the moment of inertia about an axis perpendicular to the plane is I_z = I_x + I_y.
Rolling-Motion	A combination of translational and rotational motion where v_point of contact = 0 (pure rolling).
Linear-Momentum	If the net external force on a system is zero, its total linear momentum remains constant.
Angular-Momentum	If the net external torque on a system is zero, its total angular momentum remains constant.
Vector-Product	A mathematical operation used to compute quantities like torque and angular momentum (a × b = |a||b|sinθ).
Translational-Motion	Motion in which all parts of a body move with the same velocity.
Rotational-Motion	Motion where different parts of a body move with different velocities, often involving rotation.
Pure-Rolling	Rolling motion without slipping, where the velocity of the point of contact with the surface is zero.
Rigid-Body-Dynamics	The study of forces and motions of rigid bodies under the influence of external forces and torques.

Activities

Word Search

Cross word puzzle

Lecture-1

Lecture -2 – Angular momentum and Moment of Inertia

Lecture-3 Torque

Lecture-4 – Equation of Motion of an Object moving in an Inclined plane

Lecture-5 – Problem based on translational and rotational equilbrium

Lecture – 6 – Work done by a torque