#### 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 Non-uniform Motion
- Uniformly Accelerated Motion
- Position-time, Velocity-time and Acceleration-time 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 Work-energy 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
- Stress-strain 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
- Ideal-gas 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

- How do physical laws come into existence?
- Conservation laws in physics

1. Law of conservation of energy

2. Law of conservation of linear momentum

3. Law of conservation of angular momentum

4. Law of conservation of charge

## Conservation Laws in Physics:-

The physical quantities that remain unchanged in a process are called conserved quantities. Some of the general conservation laws in nature include conservation laws of energy, mass, linear momentum, angular momentum, charge, parity, etc.

**Conservation of energy** implies that energy can be neither created nor destroyed, although it can be changed from one form (mechanical, kinetic, chemical, etc.) into another. In an isolated system, the sum of all forms of energy, therefore remains constant. For example, a falling body has a constant amount of energy, but the form of the energy changes from potential to kinetic. According to the theory of relativity, energy and mass are equivalent. Thus, the rest mass of a body may be considered a form of potential energy, part of which can be converted into other forms of energy.

**Conservation of linear momentum** expresses the fact that a body or system of bodies in motion retains its total momentum, the product of mass and velocity, unless an external force is applied to it. In an isolated system (such as the universe), there are no external forces, so momentum is always conserved. Because momentum is conserved, its components in any direction will also be conserved. Application of the law of conversation of momentum is important in solving collision problems. The operation of rockets exemplifies the conservation of momentum: the increased forward momentum of the rocket is equal but opposite in sign to the momentum of the ejected exhaust gases.

**Conservation of angular momentum** of rotating bodies is analogous to the conservation of linear momentum. Angular momentum is a vector quantity whose conservation expresses the law that a body or system that is rotating continues to rotate at the same rate unless a twisting force, called a torque, is applied to it. The angular momentum of each bit of matter consists of the product of its mass, its distance from the axis of rotation, and the component of its velocity perpendicular to the line from the axis.

**Conservation of mass** implies that matter can be neither created nor destroyed, i.e., processes that change the physical or chemical properties of substances within an isolated system (such as conversion of a liquid to a gas) leave the total mass unchanged. Strictly speaking, mass is not a conserved quantity. However, except in nuclear reactions, the conversion of rest mass into other forms of mass energy is so small that, to a high degree of precision, rest mass may be thought of as conserved.

**Conversation of charge** states that the total amount of electric charge in a system does not change with time. At a subatomic level, charged particles can be created, but always in pairs with equal positive and negative charges, so the total amount of charge always remains constant.

## NATURE OF PHYSICAL LAWS

**How Do Physical Laws Come into Existence?**

Our universe is ordered in an intelligible way. Physicists explore the universe. The range of their exploration is extremely wide: particles that are smaller than the atoms in size to the stars that are very far away. In addition to finding facts by observations and experimentation, physicists attempt to discover the laws that summarize (often as mathematical equations) these facts. When a physical phenomenon governed by the different types of forces takes place several quantities change with time, but some special quantities remain constant and such observation leads to the origin of conservative principles in Physics.

**Example:- **Suppose a ball is freely falling to the ground. Some quantities such as velocity, displacement etc. change with time, but mechanical energy (the sum of kinetic and potential energy) remains constant. And that's when we say mechanical energy is conserved under free fall.

Free fall means the force acting on the ball is the only gravitational force, however, in real conditions, air resistance also plays a big role that is a type of friction force.

The example we studied follows the following general statement:**“For motion under an external conservative force, the total mechanical energy of a body is a constant.”**

This law restricted for a conservative force should not be confused with the general law of conservation of energy of an isolated system (which is the First Law of Thermodynamics).