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
- 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
- Concept of 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
- 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
- Concept of Pressure
- Pascal's Law
- Variation of Pressure with Depth
- Atmospheric Pressure and Gauge Pressure
- Hydraulic Machines
- STREAMLINE FLOW
- Bernoulli’S Principle
- 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
- Temperature and Heat
- 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 Processes
- 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
- Behaviour of Gases
- Equation of State of a Perfect Gas
- Work Done in Compressing a Gas
- Introduction of Kinetic Theory of an Ideal Gas
- Kinetic Interpretation of Temperature
- 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
- 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
description
- Stokes’ Law
notes
Viscosity
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Viscosity is the property of a fluid that resists the force tending to cause the fluid to flow.
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It is analogous to friction in solids.
Example:-
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Consider 2 glasses one filled with water and the other filled with honey.
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Water will flow down the glass very rapidly whereas honey won’t. This is because honey is more viscous than water.
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Therefore in order to make honey flow, we need to apply a greater amount of force. Because honey has the property to resist the motion.
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Viscosity comes into play when there is relative motion between the layers of the fluid. The different layers are not moving at the same pace.
Coefficient of Viscosity
- The coefficient of viscosity is the measure of the degree to which a fluid resists flow under an applied force.
- This means how much resistance does a fluid has to its motion.
The ratio of shearing stress to the strain rate.
It is denoted by ‘η’.
Mathematically
Δt=time , displacement =Δx
Therefore,
`"shearing stress" = (Deltax)/l` where l=length
`"strain rate" =(Deltax)/(lDeltat)`
`eta="shearing stress"/"strain rate"`
`("F"/"A")/((Delta"x")/("l"Delta"t"))= ("Fl")/("vA")` where `(Deltax)/t="v"`
Therefore `eta=("Fl")/"vA"`
Unit: Poiseiulle (Pl)/Pa/Nsm-2
Dimensional Formula: [ML-1T-1]
Stokes Law
- The force that retards a sphere moving through a viscous fluid is directly ∝to the velocity and the radius of the sphere, and the viscosity of the fluid.
- Mathematically:-F =6πηrv where
- Let retarding force F∝v where v =velocity of the sphere
- F ∝ r where r=radius of the sphere
- F∝η where η=coefficient of viscosity
- 6π=constant
- Stokes law is applicable only to laminar flow of liquids.It is not applicable to turbulent law.
- Example:-Falling raindrops
- Consider a single rain drop, when rain drop is falling it is passing through air.
- The air has some viscosity; there will be some force which will try to stop the motion of the rain drop.
- Initially the rain drop accelerates but after some time it falls with constant velocity.
- As the velocity increases the retarding force also increases.
- There will be viscous force Fv and bind force Fbacting in the upward direction.There will also be Fggravitational force acting downwards.
- After some time Fg = Fr (Fv+Fb)
- Net Force is 0. If force is 0 as a result acceleration also becomes 0.
- Let retarding force F∝v where v =velocity of the sphere