Topics
Physical World
Units and Measurements
 International System of Units
 Measurement of Length
 Measurement of Mass
 Measurement of Time
 Accuracy, Precision and Least Count of Measuring Instruments
 Errors in Measurements
 Significant Figures
 Dimensions of Physical Quantities
 Dimensional Formulae and Dimensional Equations
 Dimensional Analysis and Its Applications
 Need for Measurement
 Units of Measurement
 Fundamental and Derived Units
 Length, Mass and Time Measurements
 Introduction of Units and Measurements
Physical World and Measurement
Motion in a Straight Line
 Position, Path Length and Displacement
 Average Velocity and Average Speed
 Instantaneous Velocity and Speed
 Kinematic Equations for Uniformly Accelerated Motion
 Acceleration (Average and Instantaneous)
 Relative Velocity
 Elementary Concept of Differentiation and Integration for Describing Motion
 Uniform and Nonuniform Motion
 Uniformly Accelerated Motion
 Positiontime, Velocitytime and Accelerationtime Graphs
 Position  Time Graph
 Relations for Uniformly Accelerated Motion (Graphical Treatment)
 Introduction of Motion in One Dimension
 Motion in a Straight Line
Kinematics
Motion in a Plane
 Scalars and Vectors
 Multiplication of Vectors by a Real Number or Scalar
 Addition and Subtraction of Vectors  Graphical Method
 Resolution of Vectors
 Vector Addition – Analytical Method
 Motion in a Plane
 Motion in a Plane with Constant Acceleration
 Projectile Motion
 Uniform Circular Motion (UCM)
 General Vectors and Their Notations
 Motion in a Plane  Average Velocity and Instantaneous Velocity
 Rectangular Components
 Scalar (Dot) and Vector (Cross) Product of Vectors
 Relative Velocity in Two Dimensions
 Cases of Uniform Velocity
 Cases of Uniform Acceleration Projectile Motion
 Motion in a Plane  Average Acceleration and Instantaneous Acceleration
 Angular Velocity
 Introduction of Motion in One Dimension
Laws of Motion
Laws of Motion
 Aristotle’s Fallacy
 The Law of Inertia
 Newton's First Law of Motion
 Newton’s Second Law of Motion
 Newton's Third Law of Motion
 Conservation of Momentum
 Equilibrium of a Particle
 Common Forces in Mechanics
 Circular Motion and Its Characteristics
 Solving Problems in Mechanics
 Static and Kinetic Friction
 Laws of Friction
 Inertia
 Intuitive Concept of Force
 Dynamics of Uniform Circular Motion  Centripetal Force
 Examples of Circular Motion (Vehicle on a Level Circular Road, Vehicle on a Banked Road)
 Lubrication  (Laws of Motion)
 Law of Conservation of Linear Momentum and Its Applications
 Rolling Friction
 Introduction of Motion in One Dimension
Work, Energy and Power
Motion of System of Particles and Rigid Body
Work, Energy and Power
 Introduction of Work, Energy and Power
 Notions of Work and Kinetic Energy: the Workenergy Theorem
 Kinetic Energy
 Work Done by a Constant Force and a Variable Force
 Concept of Work
 The Concept of Potential Energy
 Conservation of Mechanical Energy
 Potential Energy of a Spring
 Various Forms of Energy : the Law of Conservation of Energy
 Power
 Collisions
 Non  Conservative Forces  Motion in a Vertical Circle
Gravitation
System of Particles and Rotational Motion
 Motion  Rigid Body
 Centre of Mass
 Motion of Centre of Mass
 Linear Momentum of a System of Particles
 Vector Product of Two Vectors
 Angular Velocity and Its Relation with Linear Velocity
 Torque and Angular Momentum
 Equilibrium of Rigid Body
 Moment of Inertia
 Theorems of Perpendicular and Parallel Axes
 Kinematics of Rotational Motion About a Fixed Axis
 Dynamics of Rotational Motion About a Fixed Axis
 Angular Momentum in Case of Rotation About a Fixed Axis
 Rolling Motion
 Momentum Conservation and Centre of Mass Motion
 Centre of Mass of a Rigid Body
 Centre of Mass of a Uniform Rod
 Rigid Body Rotation
 Equations of Rotational Motion
 Comparison of Linear and Rotational Motions
 Values of Moments of Inertia for Simple Geometrical Objects (No Derivation)
Gravitation
 Kepler’s Laws
 Newton’s Universal Law of Gravitation
 The Gravitational Constant
 Acceleration Due to Gravity of the Earth
 Acceleration Due to Gravity Below and Above the Earth's Surface
 Acceleration Due to Gravity and Its Variation with Altitude and Depth
 Gravitational Potential Energy
 Escape Speed
 Earth Satellites
 Energy of an Orbiting Satellite
 Geostationary and Polar Satellites
 Weightlessness
 Escape Velocity
 Orbital Velocity of a Satellite
Properties of Bulk Matter
Thermodynamics
Mechanical Properties of Solids
 Elastic Behaviour of Solid
 Stress and Strain
 Hooke’s Law
 Stressstrain Curve
 Young’s Modulus
 Determination of Young’s Modulus of the Material of a Wire
 Shear Modulus or Modulus of Rigidity
 Bulk Modulus
 Application of Elastic Behaviour of Materials
 Elastic Energy
 Poisson’s Ratio
Mechanical Properties of Fluids
 Thrust and Pressure
 Pascal’s Law
 Variation of Pressure with Depth
 Atmospheric Pressure and Gauge Pressure
 Hydraulic Machines
 Streamline and Turbulent Flow
 Applications of Bernoulli’s Equation
 Viscous Force or Viscosity
 Reynold's Number
 Surface Tension
 Effect of Gravity on Fluid Pressure
 Terminal Velocity
 Critical Velocity
 Excess of Pressure Across a Curved Surface
 Introduction of Mechanical Properties of Fluids
 Archimedes' Principle
 Stoke's Law
 Equation of Continuity
 Torricelli's Law
Behaviour of Perfect Gases and Kinetic Theory of Gases
Oscillations and Waves
Thermal Properties of Matter
 Heat and Temperature
 Measurement of Temperature
 Idealgas Equation and Absolute Temperature
 Thermal Expansion
 Specific Heat Capacity
 Calorimetry
 Change of State  Latent Heat Capacity
 Conduction
 Convection
 Radiation
 Newton’s Law of Cooling
 Qualitative Ideas of Black Body Radiation
 Wien's Displacement Law
 Stefan's Law
 Anomalous Expansion of Water
 Liquids and Gases
 Thermal Expansion of Solids
 Green House Effect
Thermodynamics
 Thermal Equilibrium
 Zeroth Law of Thermodynamics
 Heat, Internal Energy and Work
 First Law of Thermodynamics
 Specific Heat Capacity
 Thermodynamic State Variables and Equation of State
 Thermodynamic Process
 Heat Engine
 Refrigerators and Heat Pumps
 Second Law of Thermodynamics
 Reversible and Irreversible Processes
 Carnot Engine
Kinetic Theory
 Molecular Nature of Matter
 Gases and Its Characteristics
 Equation of State of a Perfect Gas
 Work Done in Compressing a Gas
 Introduction of Kinetic Theory of an Ideal Gas
 Interpretation of Temperature in Kinetic Theory
 Law of Equipartition of Energy
 Specific Heat Capacities  Gases
 Mean Free Path
 Kinetic Theory of Gases  Concept of Pressure
 Assumptions of Kinetic Theory of Gases
 RMS Speed of Gas Molecules
 Degrees of Freedom
 Avogadro's Number
Oscillations
 Periodic and Oscillatory Motion
 Simple Harmonic Motion (S.H.M.)
 Simple Harmonic Motion and Uniform Circular Motion
 Velocity and Acceleration in Simple Harmonic Motion
 Force Law for Simple Harmonic Motion
 Energy in Simple Harmonic Motion
 Some Systems Executing Simple Harmonic Motion
 Damped Simple Harmonic Motion
 Forced Oscillations and Resonance
 Displacement as a Function of Time
 Periodic Functions
 Oscillations  Frequency
 Simple Pendulum
Waves
 Reflection of Transverse and Longitudinal Waves
 Displacement Relation for a Progressive Wave
 The Speed of a Travelling Wave
 Principle of Superposition of Waves
 Introduction of Reflection of Waves
 Standing Waves and Normal Modes
 Beats
 Doppler Effect
 Wave Motion
 Speed of Wave Motion
 Conservation of linear momentum
 Law of conservation of linear momentum
 Applications of the law of conservation of linear momentum
Notes
Law of conservation of Momentum:
From Newtons third law of motion we know that whenever a force is applied on a body there will be an equal and opposite reaction. Action and reaction forces result in change in velocities of both the bodies which in turn change the momentum of the bodies.
In an elastic collision the initial momentum of the bodies before collision is found to be equal to the final momentum of the bodies after collision.
Law of conservation of motion states that if a group of bodies are exerting force on each other. ie. Interacting with each other, their total momentum remains constant before and after the collision provided there is no external force acting on them.
Suppose two objects (two balls A and B, say) of masses m_{A} and m_{B} are travelling in the same direction along a straight line at different velocities u_{A} and u_{B}, respectively [Fig.(a)]. And there are no other external unbalanced forces acting on them. Let u_{A} > u_{B} and the two balls collide with each other as shown in Fig.(b). During collision which lasts for a time t, the ball A exerts a force F_{AB} on ball B and the ball B exerts a force F_{BA} on ball A. Suppose v_{A} and v_{B} are the velocities of the two balls A and B after the collision, respectively [Fig.(c)].
the momenta (plural of momentum) of ball A before and after the collision are m_{A}u_{A} and m_{A}v_{A}, respectively. The rate of change of its momentum (or F_{AB}) during collision will be
`"m"_"A"("v"_"A"  "u"_"A")/"t"`
Similarly, the rate of change of momentum of ball B=(F_{BA}) during the collison will be
`"m"_"B"("v"_"B"  "u"_"B")/"t"`
According to the third law of motion, the force FAB exerted by ball A on ball B and the force F_{BA} exerted by the ball B on ball A must be equal and opposite to each other. Therefore, F_{AB }= – F_{BA }or
`"m"_"A"("v"_"A"  "u"_"A")/"t"`= `"m"_"B"("v"_"B"  "u"_"B")/"t"`
This gives,
m_{A}u_{A} + m_{B}u_{B} = m_{A}v_{A} + m_{B}v_{B}
Since (m_{A}u_{A} + m_{B}u_{B}) is the total momentum of the two balls A and B before the collision and (m_{A}v_{A} + m_{B}v_{B}) is their total momentum after the collision, we observe that the total momentum of the two balls remains unchanged or conserved provided no other external force acts. As a result of this ideal collision experiment, we say that the sum of momenta of the two objects before collision is equal to the sum of momenta after the collision provided there is no external unbalanced force acting on them. This is known as the law of conservation of momentum. This statement can alternatively be given as the total momentum of the two objects is unchanged or conserved by the collision.
Notes
Conservation of Momentum

In an isolated system, the total momentum is conserved.
Example 1. In a Spinning top, total momentum = 0. For every point, there is another point on the opposite side that cancels its momentum.
Example 2. Bullet fired from a Rifle
Initially, momentum = 0
Later, the trigger is pulled, bullet gains momentum in àdirection, but this is cancelled by rifle’s ß momentum. Therefore, total momentum = 0
During the process, the chemical energy in gunpowder gets converted into heat, sound and chemical energy.
Example 3. Rocket propulsion
Initially, mass of rocket: M. It just started moving with velocity v
Initial momentum = Mv
Later, gases are ejected continuously in opposite direction with a velocity relative to rocket in downward direction giving a forward push to the rocket.
Mass of the rocket becomes (Mm)
Velocity of the rocket becomes (v + v’)
Final momentum = (M –m) (v + v’)
Thus, Mass × velocity = constant
Collision of Bodies
Let the two bodies 1 & 2 have momentum `p_1` & `p_2` before they collided with each other. After collision their momentum are `p_1’` and `p_2’` respectively.
By Newton’s Second law,
`F = (dp)/(dt)`
For 1: `F_(12) = (p_1’ – p_1) /(∆t)`
For 2: `F_(21) = (p_2’ – p_2) /(∆t)`
By Newton’s Third law,
`F _(12) =  F_(21)`
`(p_1’ – p_1)/(∆t) = (p_2’ – p_2) /(∆t)`
`(p_1’ – p_1) = (p_2’ – p_2)`
`p_1’ + p_2’ = p_1 + p_2`
Conclusion:
Final momentum of the system = Initial momentum of the system
Problem: A railway truck A of mass 3 × 104 kg travelling at 0.6 m/s collides with another truck B of half its mass moving in the opposite direction with a velocity of 0.4 m/s. If the trucks couple automatically on collision, find the common velocity with which they move.
Solution.
M_{1} = 3 × 104 kg
m_{2} = ½ of mass of A = 1.5 × 104 kg
u_{1} = 0.6 m/s
u_{2} = 0.4 m/s
Before collision:
m_{1}u_{1} + m_{2}u_{2} = 3 × 104 × 0.6 + 1.5 × 104 ×(0.4) = 1.2 × 104 kg m/s
After collision:
(m_{1}+ m_{2}) v = 4.5 × 104v kg m/s
As per conservation of momentum,
1.2 × 104 = 4.5 × 104v
V = 1.2/ 4.5 = 0.27 m/s
Therefore, the common velocity is 0.27m/s