Topics
Units and Measurements
- Quantitative Science
- System of Units
- Derived Quantities and Units
- Rules and Conventions for Writing SI Units and Their Symbols
- Measurement of Length
- Measurement of Mass
- Measurement of Time
- Dimensions and Dimensional Analysis
- Accuracy, Precision and Uncertainty in Measurement
- Errors in Measurements>Systematic Errors
- Errors in Measurements>Random Errors
- Estimation of Errors
- Combination of Errors
- Significant Figures
- Definitions of SI Units and Constants
Mathematical Methods
- Vector Analysis
- Scalar
- Vector
- Vector Operations>Multiplication of a Vector by a Scalar
- Vector Operations>Addition and Subtraction of Vectors
- Vector Operations>Triangle Law for Vector Addition
- Vector Operations>Law of parallelogram of vectors
- Resolution of Vectors
- Multiplication of Vectors
- Scalar Product(Dot Product)
- Vector Product (Cross Product)
- Concept of Calculus
- Differential Calculus
- Integral Calculus
Motion in a Plane
- Concept of Motion
- Rectilinear Motion
- Displacement
- Path Length
- Average Velocity
- Average Speed
- Instantaneous Velocity
- Instantaneous Speed
- Acceleration in Linear Motion
- Relative Velocity
- Motion in Two Dimensions-Motion in a Plane
- Average and Instantaneous Velocities
- Acceleration in a Plane
- Equations of Motion in a Plane with Constant Acceleration
- Relative Velocity in Two Dimensions
- Projectile Motion
- Uniform Circular Motion (UCM)
- Key Parameters of Circular Motion
- Centripetal Acceleration
- Conical Pendulum
Laws of Motion
- Fundamental Principles of Motion and Mechanics
- Types of Motion
- Aristotle’s Fallacy
- Newton’s Laws of Motion
- Newton's First Law of Motion
- Newton’s Second Law of Motion
- Newton's Third Law of Motion
- Inertial and Non-inertial Frames of Reference
- Types of Forces>Fundamental Forces in Nature
- Types of Forces>Contact and Non-Contact Forces
- Types of Forces>Real and Pseudo Forces
- Types of Forces>Conservative and Non-Conservative Forces
- Types of Forces>Work Done by a Variable Force
- Work Energy Theorem
- Principle of Conservation of Linear Momentum
- Collisions
- Elastic and Inelastic Collisions
- Perfectly Inelastic Collision
- Coefficient of Restitution e
- Expressions for Final Velocities in Elastic Head-On Collision
- Loss of Kinetic Energy in Perfectly Inelastic Head-On Collision
- Collision in Two Dimensions
- Impulse of a Force
- Necessity of Defining Impulse
- Rotational Analogue of a Force: Moment of a Force Or Torque
- Couple and Its Torque
- Proof of Independence of the Axis of Rotation
- Mechanical Equilibrium
- States of Equilibrium
- Centre of Mass>Mathematical Understanding of Centre of Mass
- Centre of Mass>Velocity of Centre of Mass
- Centre of Mass>Acceleration of Centre of Mass
- Centre of Mass>Characteristics of Centre of Mass
- Centre of Gravity
Gravitation
- Concept of Gravitation
- Kepler’s Laws
- Law of Orbit or Kepler's First Law
- Law of Areas or Kepler's Second Law
- Law of Periods or Kepler's Third Law
- Newton's Universal Law of Gravitation
- Measurement of the Gravitational Constant (G)
- Acceleration Due to Gravity (Earth’s Gravitational Acceleration)
- Variation in the Acceleration>Variation in Gravity with Altitude
- Variation in the Acceleration>Variation in Gravity with Depth
- Variation in the Acceleration>Variation in Gravity with Latitude and Rotation of the Earth
- Variation in the Acceleration>Effect of the shape of the Earth
- Gravitational Potential Energy
- Expression for Gravitational Potential Energy
- Connection of Potential Energy Formula with mgh
- Potential and Potential Difference
- Escape Velocity
- Earth Satellites
- Projection of Satellite
- Weightlessness in a Satellite
- Time Period of Satellite
- Binding Energy of an Orbiting Satellite
Mechanical Properties of Solids
- Mechanical Properties of Solids
- Elastic Behavior of Solids
- Stress and Strain
- Types of Stress and Corresponding Strain
- Hooke’s Law
- Elastic Modulus>Young’s Modulus
- Elastic Modulus>Bulk Modulus
- Elastic Modulus>Modulus of Rigidity
- Elastic Modulus>Poisson’s Ratio
- Stress-strain Curve
- Strain Energy
- Hardness of Material
- Friction in Solids
- Origin of Friction
- Types of Friction>Static Friction
- Types of Friction>Kinetic Friction
- Types of Friction>Rolling Friction
Thermal Properties of Matter
- Thermal Properties of Matter
- Temperature and Heat
- Measurement of Temperature
- Absolute Zero and Absolute Temperature
- Ideal Gas Equation
- Thermal Expansion
- Linear Expansion
- Areal Expansion
- Volume Expansion
- Relation Between Coefficient of Expansion
- Specific Heat Capacity
- Specific Heat Capacity of Solids and Liquids
- Specific Heat Capacity of Gas
- Heat Equation
- Thermal Capacity
- Calorimetry
- Change of State
- Analysis of Observation>From Point A to B
- Analysis of Observation>From Point B to D
- Temperature Effects and Considerations
- Evaporation vs Boiling
- Boiling Point and Pressure
- Factors Affecting Cooking
- Sublimation
- Phase Diagram
- Gas and Vapour
- Latent Heat
- Heat Transfer
- Conduction
- Thermal Conductivity
- Coefficient of Thermal Conductivity
- Thermal Resistance
- Applications of Thermal conductivity
- Convection
- Application of Convection
- Free and Forced Convection
- Radiation
- Newton’s Law of Cooling
Sound
- Sound Waves
- Common Properties of All Waves
- Transverse Waves
- Longitudinal Waves
- Mathematical Expression of a Wave
- The Speed of Travelling Waves
- The Speed of Transverse Waves
- The Speed of Longitudinal Waves
- Newton's Formula for Velocity of Sound
- Laplace’s Correction
- Factors Affecting Speed of Sound
- Principle of Superposition of Waves
- Echo
- Reverberation
- Acoustics
- Qualities of Sound
- Doppler Effect
- Source Moving and Listener Stationary
- Listener Approaching a Stationary Source with Velocity
- Both Source and Listener are Moving
- Common Properties between Doppler Effect of Sound and Light
- Major Differences between Doppler Effects of Sound and Light
Optics
- Fundamental Concepts of Light
- Nature of Light
- Ray Optics Or Geometrical Optics
- Cartesian Sign Convention
- Reflection>Reflection from a Plane Surface
- Reflection>Reflection from Curved Mirrors
- Total Internal Reflection
- Refraction of Light
- Applications of Total Internal Reflection
- Refraction at a Spherical Surface and Lenses
- Thin Lenses and Their Combination
- Refraction at a Single Spherical Surface
- Lens Makers' Equation
- Dispersion of Light
- Analysis of Prism
- Thin Prisms
- Some Natural Phenomena Due to Sunlight
- Defects of Lenses
- Optical Instruments
- Simple Microscope or a Reading Glass
- Compound Microscope
- Telescope
Electrostatics
- Concept of Electrostatics
- Electric Charge
- Basic Properties of Electric Charge
- Additive Nature of Charge
- Quantization of Charge
- Conservation of Charge
- Force between Charges
- Coulomb’s Law
- Scalar Form of Coulomb’s Law
- Relative Permittivity or Dielectric Constant
- Definition of Unit Charge from the Coulomb’s Law
- Coulomb's Law in Vector Form
- Principle of Superposition
- Electric Field
- Electric Field Intensity Due to a Point-Charge
- Practical Way of Calculating Electric Field
- Electric Lines of Force
- Electric Flux
- Gauss’s Law
- Electric Dipole
- Couple Acting on an Electric Dipole in a Uniform Electric Field
- Electric Intensity at a Point Due to an Electric Dipole
- Continuous Charge Distribution
Electric Current Through Conductors
- Concept of Electric Currents in Conductors
- Electric Current
- Flow of Current Through a Conductor
- Drift Speed
- Ohm's Law
- Limitations of Ohm’s Law
- Electrical Power
- Resistors
- Rheostat
- A combination of resistors in both series and parallel
- Specific Resistance
- Variation of Resistance with Temperature
- Electromotive Force (emf)
- Cells in Series
- Cells in Parallel
- Types of Cells
Magnetism
- Concept of Magnetism
- Magnetic Lines of Force
- The Bar Magnet
- Magnetic Field due to a Bar Magnet
- Magnetic Field Due to a Bar Magnet at an Arbitrary Point
- Gauss' Law of Magnetism
- The Earth’s Magnetism
Electromagnetic Waves and Communication System
- Foundations of Electromagnetic Theory
- EM Wave
- Sources of EM Waves
- Characteristics of EM Waves
- Electromagnetic Spectrum
- Radio Waves
- Microwaves
- Infrared waves
- Visible Light
- Ultraviolet rays
- X-rays
- Gamma Rays
- Propagation of EM Waves
- Ground (surface) Wave
- Space wave
- Sky wave propagation
- Communication System
- Elements of a Communication System
- Commonly Used Terms in Electronic Communication System
- Modulation
Semiconductors
- Concept of Semiconductors
- Electrical Conduction in Solids
- Band Theory of Solids
- Intrinsic Semiconductor
- Extrinsic Semiconductor
- n-type semiconductor
- p-type semiconductor
- Charge neutrality of extrinsic semiconductors
- p-n Junction
- A p-n Junction Diode
- Basics of Semiconductor Devices
- Applications of Semiconductors and P-n Junction Diode
- Thermistor
- Introduction
- Definition: Kinetic Friction
- Formula: Kinetic Friction
- Formula: Coefficient of Kinetic Friction
- Characteristics
- Laws of Kinetic Friction
- Coefficient of Kinetic Friction for Different Materials
- Mechanism of Kinetic Friction
- Significance
Introduction
Kinetic friction is the force of resistance that acts when one body slides over another surface. Once an object starts moving, the friction force decreases compared to what was needed to initiate the motion. The force required to maintain steady sliding motion is less than the force required to overcome static friction and start the motion.
Definition: Kinetic Friction
Friction between two surfaces in contact when one body is actually sliding over the other body is called kinetic friction or dynamic friction.
or
The force of friction that comes into play when a body is in a steady state of motion over another surface is called the force of kinetic friction.
Formula: Kinetic Friction
Fₖ = μₖ N
Where:
- Fₖ = Force of kinetic friction
- μₖ = Coefficient of kinetic friction (constant of proportionality)
- N = Normal reaction between the two surfaces in contact
Formula: Coefficient of Kinetic Friction
μₖ = Fₖ/N
The coefficient of kinetic friction is defined as the ratio of force of kinetic friction to the normal reaction between the two surfaces in contact.
Characteristics
- The force of kinetic friction is directly proportional to the normal reaction between two surfaces in contact
- Kinetic friction is independent of the shape and apparent area of the surfaces in contact
- It depends upon the nature and material of the surfaces in contact
- The magnitude of kinetic friction is independent of the relative velocity between the object and the surface (provided the velocity is neither too large nor too small)
- Kinetic friction acts in the direction opposite to the relative motion between surfaces
Laws of Kinetic Friction
First Law:
The force of kinetic friction (Fₖ) is directly proportional to the normal reaction between two surfaces in contact.
- Fₖ ∝ N
- Fₖ = μₖ N
Second Law:
The coefficient of kinetic friction is defined as the ratio of the force of kinetic friction to the normal reaction between the two surfaces in contact.
-
μₖ = Fₖ/N
Third Law:
The force of kinetic friction is independent of shape and apparent area of the surfaces in contact.
Fourth Law:
The force of kinetic friction depends upon the nature and material of the surfaces in contact.
Fifth Law:
The magnitude of the force of kinetic friction is independent of the relative velocity between the object and the surface (provided that the relative velocity is neither too large nor too small).
Coefficient of Kinetic Friction for Different Materials
| Material Pair | Coefficient of Kinetic Friction (μₖ) |
|---|---|
| Rubber on concrete (dry) | 0.25 |
| Glass on glass | 0.40 |
| Brass on steel | 0.40 |
| Copper on steel | 0.44 |
| Aluminium on steel | 0.47 |
| Steel on steel | 0.57 |
| Teflon on Teflon | 0.80 |
Mechanism of Kinetic Friction
When a body slides across a surface, kinetic friction opposes its motion. At the microscopic level, even smooth surfaces have irregularities. As one surface slides over another, these irregularities interlock and create resistance. This resistance is the kinetic friction force.
Key Points to Remember
- Kinetic friction acts only when there is relative motion between two surfaces
- Direction: Kinetic friction always acts opposite to the direction of relative motion
- Magnitude: The magnitude depends only on the normal force and the nature of the surfaces, not on the area of contact or the speed of sliding
- Coefficient remains constant for a given pair of materials (under normal conditions)
Why Kinetic Friction is Less than Static Friction
Once sliding begins, the surfaces are in continuous contact at different points. The deformation of surface irregularities is less severe than when initiating motion from rest. This results in a lower kinetic friction coefficient (μₖ) compared to the static friction coefficient (μₛ), meaning less force is needed to maintain motion than to start motion.
Significance
- Kinetic friction is essential in understanding the motion of objects on surfaces
- It helps in calculating the deceleration of moving objects
- Important for designing braking systems in vehicles
- Used in industrial processes involving sliding and movement
- Understanding kinetic friction helps in friction reduction and lubrication techniques
- Critical for safety analysis in transportation and machinery
- Helps predict energy loss due to friction in mechanical systems
