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 NonUniform Motion
 Uniformly Accelerated Motion
 Positiontime, Velocitytime and Accelerationtime Graphs
 Motion in a Straight Line  Positiontime 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 WorkEnergy 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
 Idealgas 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
 Friction
notes
Common forces in Mechanics
Contact & Noncontact forces
External force comes into picture when the body starts moving or comes to rest either by coming in contact with the body or without being in contact.
Contact force Force applied by coming in contact with the body
Example: hitting of cricket ball with bat in game
Noncontact force Force applied without coming in contact with body
Example: Coin attracted towards magnet (magnetic force)
Ball dropped at height attracted towards the earth (gravitational force)
Weight of a body: It is the force with which earth attracts a body towards its centre. If M is a mass of body and g is acceleration due to gravity, weight of the body is mg in vertically downward direction.
Normal Force: If two bodies are in contact a contact force arises, if the surface is smooth the direction of force is normal to the plane of contact. We call this force as Normal Force.
Example: Let us consider a book resting on the table. It is acted upon its weight in vertically downward direction and is at rest. It means there is another force acting on the block in opposite direction, which balances its weight. This force is provided by the table and we call it as normal force.
Tension in string: Suppose a block is hanging from a string. Weight of the block is acting vertically downward but it is not moving, hence its weight is balanced by a force due to string. This force is called ‘Tension in string’. Tension is a force in a stretched string. Its direction is taken along the string and away from the body under consideration.
Simple pulley
Consider two bodies of masses m1 and m2 tied at the ends of an extensible string, which passes over a light and friction less pulley. Let m1 > m2. The heavier body will move downwards and the lighter will move upwards. Let a be the common acceleration of the system of two bodies, which is given by
`a=((m_1  m_2)g)/(m_1 + m_2)`
Tension in the string is given by
`T=(2m_1m_2 × g)/(m_1+m_2)`
Apparent Weight and Actual Weight:
Apparent weight of a body is equal to its ‘actual weight’ if the body is either in a state of rest or in a state of uniform motion.
"Apparent weight of a body for vertical upward accelerated motion is given as
Apparent weight= Actual weight ma = m(g+a)"
"Apparent weight of a body for vertically downward accelerated motion is given as
Apparent weight= Actual weight ma = m(ga)"
Friction

Friction is a contact force that opposes relative motion.

No friction exists till an external force is applied.
Angle of Friction:
The angle made by the resultant reaction force with the vertical (normal reaction) is known as the angle of the friction.
Now, in the triangle OAB
`(AB)/(OB) = cot θ`
So, `OB = (AB)/ (cot θ) = AB tan θ`
Or,` tan θ = (OB)/(AB) = f / N`
So, `tan θ=f / N = µs`
Angle of Repose:
"It is the angle which an inclined plane makes with the horizontal so that a body placed over it just begins to slide of its own accord."
Consider a body of mass m resting on an inclined plane of inclination q. The forces acting on the body are shown –
`F_f` being the force of friction. If friction is large enough, the body will not slide down.
Along x: mg sin θ – f = 0 …(1)
Along y: N –mg cos θ = 0 …(2)
i.e. N = mg cos θ and f = mg sin θ
Thus, f ≤ µs N gives,
mg sin θ ≤ mg cos θ
So, tan θ ≤ µs . This signifies, the coefficient of static friction between the two surfaces, in order that the body doesn’t slide down.
When q is increased, then tan θ >. Thus sliding begins, and the angle θr = tan1 µ. This angle is known as the angle of repose.
Problem 1: Calculate the force required for pushing a 30 kg wooden bar over a wooden floor at a constant speed. Coefficient of friction of wood over wood = 0.25
Solution.
M = 30 kg
μ = 0.25
`(F_a– f) = ma`
For constant speed, a = 0
So, `F_a = f= μN`
From free body diagram, N = mg
Therefore, `F_a = f= μN = μmg = 0.25 × 30 × 9.8 = 73.5 N`
Problem 2: A homogenous chain of length L lies on a table. What is the maximum length l of the part of the chain hanging over the table if the coefficient of friction between the chain and the table is u, the chain remaining at rest with the table?Solution.
Let ρ be the mass per unit length of the chain
`Ρ = m/l` or, m = ρl
Weight of hanging part = W2 = ρlg
Weight of chain over the table = W1 = ρ(Ll)g
For equilibrium,
R = ρ(Ll)g  (i)
f= W2 = ρlg
μR = ρlg (ii)
(i) Divided by (ii) gives
`1/μ = (Ll)/l`
`l = μL – μl`
`l + μl = μL`
Therefore, `l = (μL)/( μ + 1)`
Friction A boon or Bane against motion
Friction is a boon because of its advantages like:

Friction helps in walking
When we walk, we push the ground backwards with one foot. According to Newton’s Third law, there is an equal and opposite force exerted by the ground. This force is exerted on a comparatively smaller mass i.e. our foot. So, acceleration is increases. Hence the other foot gets accelerated.
If there is no friction, we will slip and can’t walk.

Friction helps in movement of automobiles
Friction is a bane because of its disadvantages:

A good amount of useful energy is wasted as heat in various machine parts

Noise produced in machines

Engines of automobiles consume more fuel
Methods to reduce Friction:

Use of Lubricants
Use of Grease:

Use of Ball bearing

Ball bearings are kind of rolling elements that use small freely rotating metal balls which reduce friction.
Design modification of different parts of machine to reduce friction.