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
Static friction
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Static friction is the force of friction between two surfaces so long as there is no relative motion between them. It is always equal to the applied force.
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Force that resists initiation of motion of one body over another with which it is in contact
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Opposes Impending motion
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Denoted by fs
Let the ball be at rest initially
Applied force, Fa = 0; Static friction, fs = 0
Later, applied force, Fa = F, then fs also increases but only up to a certain limit. As soon as Fa becomes greater than fs, the ball starts to move.
Fs acts when a body is at rest. Hence called Static friction.
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Limiting value of fs depends on Normal reaction, and is independent of the area of contact
fs max ∝ N
fs max = constant × N
fs max = μs N
where μs is the coefficient of static friction
This coefficient depends on the nature of surfaces in contact.
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According to the Law of Static friction, Static friction is always less than or equal to the limiting value of fs
fs =< fs max
fs max = μs N
fs =< μs N
Kinetic friction
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Kinetic friction is the force of friction which comes into play between two surfaces when there is some relative motion between them.
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Force that resists motion of one body over another with which it is in contact.
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Denoted by fk
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As motion starts, fs vanishes and fk appears
Kinetic friction is Independent of the area of contact and velocity of the body
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It varies with Normal reaction, N
fk ∝ N
fk = constant × N
fk = μk N; μk is the coefficient of kinetic friction
Three scenarios can arise in a body’s motion
1. When applied force > fk
Fa > fk
(Fa – fk) = ma
a = (Fa – fk)/m
2. When applied force = fk
Fa = fk
Therefore, a = 0 i.e. the body moves with uniform velocity
3. When applied force = 0
Fa = 0
A = - fk/m
No motion occurs, the body stops
Relation between Coefficient of Static & Kinetic friction
fk = μk N
fs =< μs N
fs > fk (to keep the body moving)
μs N > μk N
Or, μk < μs
Coefficient of kinetic friction is smaller than the coefficient of static friction.
