#### Topics

##### Physical World and Measurement

##### Physical World

##### Units and Measurements

- International System of Units
- Measurement of Length
- Measurement of Mass
- Measurement of Time
- Accuracy Precision of Instruments and Errors in Measurement
- 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

##### Kinematics

##### Motion in a Plane

- Scalars and Vectors
- Multiplication of Vectors by a Real Number
- 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
- General Vectors and Their Notations
- Motion in a Plane - Average Velocity and Instantaneous Velocity
- Rectangular Components
- Scalar and Vector 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

##### 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
- Relative Velocity
- Elementary Concepts of Differentiation and Integration for Describing Motion
- Uniform and Non-Uniform Motion
- Uniformly Accelerated Motion
- Position-time, Velocity-time and Acceleration-time Graphs
- Motion in a Straight Line - Position-time Graph
- Relations for Uniformly Accelerated Motion (Graphical Treatment)
- Introduction

##### 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

##### 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
- The 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

##### Motion of System of Particles and Rigid Body

##### 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 Bodies
- 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 Surface of Earth
- 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

##### Mechanical Properties of Fluids

- Thrust and Pressure
- Transmission of Pressure in Liquids: Pascal’s Law
- Variation of Pressure with Depth
- Atmospheric Pressure and Gauge Pressure
- Hydraulic Machines
- STREAMLINE FLOW
- Applications of Bernoulli’s Equation
- Viscous Force Or Viscosity
- Reynolds Number
- Surface Tension
- Effect of Gravity on Fluid Pressure
- Terminal Velocity
- Critical Velocity
- Excess of Pressure Across a Curved Surface
- Introduction to Fluid Machanics
- Archimedes' Principle
- Stokes' Law
- Equation of Continuity
- Torricelli'S Law

##### 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 Blackbody Radiation
- Wein'S Displacement Law
- Stefan's Law
- Anomalous Expansion of Water
- Liquids and Gases
- Thermal Expansion of Solids
- Green House Effect

##### Mechanical Properties of Solids

##### 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 Engines
- Refrigerators and Heat Pumps
- Second Law of Thermodynamics
- Reversible and Irreversible Processes
- Carnot Engine
- Isothermal Processes
- Adiabatic Processes

##### Behaviour of Perfect Gases and Kinetic Theory of Gases

##### 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
- Kinetic Theory of Gases- Assumptions
- rms Speed of Gas Molecules
- Degrees of Freedom
- Avogadro's Number

##### Oscillations and Waves

##### Oscillations

- Periodic and Oscillatory Motions
- Simple Harmonic Motion (SHM)
- 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

##### Waves

#### notes

## Acceleration

It is the rate of change of velocity with time. The only two ways to accelerate is by changing the speed or change in direction or change both. It is a vector quantity. If the velocity of the object increases with time, its acceleration increases. If the velocity of an object decreases with time, its acceleration is negative.

The motion is uniformly accelerated motion or non-uniformly accelerated, depending on how the velocity changes with time. It is uniform for a body if the velocity changes by equal amounts in equal intervals and if its velocity changes by unequal amounts, it is non-uniform.

Acceleration = Change in velocity/time taken

Its unit is m/s².

Constant speed does not guarantee that acceleration is zero. For example, a body moving with constant speed in a circle changes its velocity every instant and hence its acceleration is not equal to zero.

Velocity is a quantity having both magnitude and direction, a change in velocity may involve either or both of these factors. Acceleration may result from a change in speed, a change in direction or changes in both. Like velocity, acceleration can also be positive, negative or zero.

Motion in Different Acceleration for Different Time Intervals

Let’s understand this through an example. Suppose, a particle started its motion from rest with an acceleration of 1m/s² for 2s and then continued it for next 1s changing to 2m/s². The distance travelled during this will be:

After 2s the velocity is, v = u + at = 2 m/s

Now, if this is the initial velocity for the second half of the motion, `s_2=ut+`1/2`at²=3 m`

Distance travelled in first half is: `s_1 = 0+1/2at²= 2 m`

Hence total distance travelled = `s_1+s_2`= 5 m

On a plot of velocity versus time, the average acceleration is the slope of the straight line connecting the points corresponding to (`v_2, t_2) and (v_1, t_1`). The average acceleration for velocity-time graph shown above for different time intervals 0 s- 10 s, 10 s – 18 s, and 18 s – 20 s are:

`0s - 10s`, `bar a=((24-0)ms^-1)/((10-0)s)=2.4 ms^-1`

`10s - 18s`, `bar a=((24-24)ms^-1)/((18-10)s)=0 ms^-1`

`18s - 20s`, `bar a=((0-24)ms^-1)/((20-18)s)=2.4 ms^-1`

Let us see how velocity-time graph looks like for some simple cases as shown below. The shows velocity time graph for motion with constant acceleration for the following cases:

(a) An object is moving in a positive direction with a positive acceleration, for example the motion of the car between t = 0 s and t = 10 s.

(b) An object is moving in positive direction with a negative acceleration, for example, motion of the car between t = 18 s and 20 s.

(c) An object is moving in negative direction with a negative acceleration, for example the motion of a car moving from O in negative x-direction with increasing speed.

(d) An object is moving in positive direction till time `t_1`, and then turns back with the same negative acceleration, for example the motion of a car from point O to point Q till time `t_1` with decreasing speed and turning back and moving with the same negative acceleration.

**Average Acceleration**

It is the change in velocity divided by an elapsed time. For instance, if the velocity of a marble increases from 0 to 60 cm/s in 3 seconds, its average acceleration would be 20 cm/s². This means that the marble’s velocity will increase by 20 cm/s every second.

It is the rate of change of velocity with respect to displacement

Acceleration is `a = ``(dv)/dt`

∴ `a =` `(dv)/(dx/v)`

`a = v``((dv)/dx)`

Freefall object experiences an acceleration of g= 9.8m/s² in a downward direction that is towards the center of the earth. In upward direction it is -g = -9.8m/s²