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General Physics I:
Sunil Karna
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Front Matter
Colophon
Dedication
Acknowledgements
Preface
1
Units and Measurements
1.1
Physical Quantities
1.1.1
Derived Units
1.1.1.1
Dimensional Analysis
1.1.2
Errors in Measurement
1.1.3
Significant Figures
1.1.3.1
Rounding off the Numbers
1.1.3.2
Mathematical Operations with Significant Figures
1.2
Examples
1.3
Exercise
2
Vectors
2.1
Algebra of Vectors
2.1.1
Components of a Vector:
2.1.2
Product of Two Vectors:
2.1.2.1
Scalar (or Dot) Product
2.1.2.2
Vector (or Cross) Product
2.1.3
Transformation of Axis
2.2
Examples
2.3
Exercise
3
Motion
3.1
1D Kinematics
3.1.1
Analyzing the motion curve
3.1.1.1
Reading of
\(x \sim t\)
graph
3.1.2
Equations of Motion
3.1.3
Relative velocity
3.1.4
Rules to follow while solving motion problems:
3.2
Examples A
3.3
2D Kinematics
3.3.1
Projtile Motion
3.3.2
Circular Kinematics
3.3.2.1
Centripetal Acceleration:
3.3.2.2
Angular Displacement,
\(\theta\text{:}\)
3.3.2.3
Angular Velocity,
\(\omega\text{:}\)
3.3.2.4
Angular Frequency,
\(\omega\text{:}\)
3.3.2.5
Angular Acceleration,
\(\alpha\text{:}\)
3.3.3
Motion in Polar Coordinates
3.4
Examples B
3.5
Exercise
4
Force and Equilibrium
4.1
Types of Forces
4.1.1
Fundamental and Mechanical Forces
4.1.2
Newton’s Laws of Motion
4.1.3
Friction
4.1.4
Statics
4.1.4.1
Static Equilibrium
4.2
Examples A
4.3
Translational Equilibrium
4.4
Examples B
4.5
Dynamics
4.5.1
Atwood’s Machine
4.5.2
Motion in Air Drag
4.6
Examples C
4.7
Circular Motion
4.7.1
Horizontal Circle
4.7.2
Vertical Circle
4.8
Banking of a Curve
4.9
Examples D
4.10
Center of Mass
4.11
Torque
4.11.1
Rotational Equilibrium
4.11.2
States of Equilibrium
4.12
Examples E
4.13
Exercise
5
Energy and Collision
5.1
Work, Energy, and Power
5.1.1
Work
5.1.2
Energy
5.1.2.1
Work-Energy Theorem
5.1.2.2
Kinetic Energy:
5.1.2.3
Potential Energy:
5.1.3
Conservative and Non-Conservative Forces
5.1.4
Principle of Conservation of Energy
5.1.5
Energy Diagram
5.1.6
Loop-the-Loop Track
5.2
Power
5.2.1
Simple Machine
5.2.2
Pulley
5.2.2.1
Mechanical Advantage
5.2.2.2
Types of Pulley
5.3
Examples A
5.4
Impulse and Momentum
5.4.1
Collision
5.4.1.1
Inelastic Collision
5.4.1.2
Elastic Collision
5.4.1.3
Collision in 2D
5.4.1.4
Coefficient of Restitution, e
5.4.2
Ballistic Pendulum
5.5
Examples B
5.6
Exercise
6
Gravitation
6.1
Newton’s Law of Gravitation
6.1.1
Acceleration Due to Gravity,
\(g\)
6.1.1.1
Effect of the Rotation of the Earth on g
6.1.1.2
Effect of Altitude of the Earth on g
6.1.1.3
Effect of Depth of the Earth on g
6.1.2
Gravitational Potential Energy, U
6.1.3
Orbital Velocity of a Satelite
6.1.4
Escape Velocity
6.1.5
Geosynchronous satellite
6.2
Kepler’s Laws of Planetary Motion
6.2.1
Polar Coordinates
6.2.2
Derivation of Kepler’s I Law
6.2.3
Derivation of Kepler’s II Law
6.2.4
Derivation of Kepler’s III Law
6.3
Examples
6.4
Exercise
7
Rigid Body
7.1
Moment of Inertia
7.1.1
Parallel axis theorem
7.1.2
Perpendicular axis theorem
7.1.3
Moment of Inertia of a Ring or Hoop
7.1.3.1
About an axis passing through its center of mass and perpendicular to its plane
7.1.3.2
About an axis passing through its rim and perpendicular to its plane
7.1.3.3
About an axis through its diameter
7.1.4
Moment of Inertia of a Rod
7.1.4.1
About an axis passing through its center of mass and perpendicular to its plane
7.1.4.2
About an axis passing through its one edge and perpendicular to its plane
7.1.4.3
About an axis passing along its length and through the center of mass
7.1.5
Moment of Inertia of a Disk
7.1.5.1
About an axis passing through its center of mass and perpendicular to its plane
7.1.5.2
About an axis through its diameter
7.1.5.3
About an axis passing through its edge and perpendicular to its plane
7.1.6
Moment of Inertia of a Plate
7.1.6.1
About an axis
\(I_{x}\)
passing through its center of mass and parallel to its plane
7.1.6.2
About an axis
\(I_{y} \)
passing through its center of mass and parallel to its plane
7.1.6.3
About an axis passing through its center of mass and perpendicular to its plane
7.1.7
Moment of Inertia of a Cylinder
7.1.7.1
Moment of inertia of a thin hollow cylinder about an axis passing through its center of mass and perpendicular to its plane
7.1.7.2
Moment of inertia of a thick hollow cylinder about an axis passing through its center of mass and perpendicular to its plane
7.1.7.3
Moment of inertia of a solid cylinder about an axis passing through its center of mass and perpendicular to its plane
7.1.8
Moment of Inertia of a Cone
7.1.8.1
Moment of Inertia of a Solid Cone about an axis of symmetry
7.1.8.2
Moment of Inertia of a Solid Cone about a Vertex Parallel to the Base
7.1.8.3
Moment of Inertia of a Hollow Cone about an axis of symmetry
7.1.9
Moment of Inertia of a Sphere
7.1.9.1
Moment of inertia of a hollow sphere about its diameter
7.1.9.2
Moment of inertia of a solid sphere about its diameter
7.1.10
Radius of Gyration
7.2
Examples A
7.3
Rotational Dynamics
7.3.1
Rotational Overview
7.3.2
Rotational Energy, Work, and Power
7.3.3
Angular Momentum
7.3.4
The Gyroscope
7.4
Examples B
7.5
Oscillatory Motion
7.5.1
Simple Harmonic Motion
7.5.1.1
Equation of SHM
7.5.1.2
Energy in SHM
7.5.2
Simple Pendulum
7.5.3
Compound Pendulum
7.5.4
Simple Pendulum with Large Angle Approximation
7.6
Examples C
7.7
Exercise
8
Elasticity
8.1
Hooke’s Law
8.1.1
Elastic Modulus
8.1.1.1
Young’s Modulus or Elasticity of Length
8.1.1.2
Bulk Modulus or Elasticity of Volume
8.1.1.3
Shear Modulus (Modulus of Rigidity) or Elasticity of Shape
8.1.2
Hook’s Law for a Spring
8.1.3
Elastic Potential Energy
8.2
Examples A
8.3
Exercise
9
Fluid Mechanics
9.1
Fluid Statics
9.1.1
Pascal’s Principle
9.1.1.1
Measurement of Fluid Pressure
9.1.2
Archimedes’ Principle
9.2
Fluid Flow
9.2.1
Equation of Continuity
9.2.2
Bernoulli’s Principle
9.2.3
Applications of Bernoulli’s Principle:
9.3
Examples A
9.4
Viscosity
9.4.1
Coefficient of Viscosit
9.4.2
Poiseuille’s Law
9.4.3
Stoke’s Law
9.4.3.1
Terminal velocity of a body moving through a fluid
9.5
Surface Tension
9.5.1
Capillary Action
9.5.2
Equivalence between surface tension and surface energy
9.5.3
Soap Bubble
9.6
Examples B
9.7
Exercise
10
Heat and Thermodynamics
10.1
Heat
10.1.1
Temperature and Thermometers
10.1.2
Absolute Scale
10.2
Thermal Expansion
10.2.1
Linear Expansion
10.2.2
Superficial Expansion
10.2.3
Volumetric (Cubic) Expansion
10.2.4
Relation between
\(\alpha, \,\beta,\)
and
\(\gamma\)
10.2.5
Anomalous expansion of water
10.3
Quantity of Heat
10.3.1
Specific Heat Capacity
10.3.2
Latent Heat
10.3.3
Phase Changes of Matter
10.3.4
Calorimetry
10.3.5
Triple Point of Water
10.3.6
Heat Transfer
10.3.7
Newton’s Law of Cooling
10.3.8
Solar Constant
10.4
Examples A
10.5
Kinetic Theory of Ideal Gas
10.5.1
Pressure of an Ideal Gas
10.5.2
Degree of Freedom:
10.5.3
Law of Equipartition of Energy
10.5.3.1
Avogadro’s Number,
\(N_{A}\)
10.5.3.2
Atomic Mass Unit, u
10.5.4
Internal Energy of a Gas
10.5.5
Gas Laws
10.6
Thermodynamics
10.6.1
Thermodynamical Variables
10.6.2
Laws of Thermodynamics
10.6.2.1
Zeroth Law of Thermodynamics
10.6.2.2
First Law of Thermodynamics
10.6.3
Application of I law of thermodynamics
10.6.4
Second Law of Thermodunamics
10.6.5
Heat Engines
10.6.6
Carnot’s Heat Engine
10.6.7
Reversible Heat Engines
10.6.8
Carnot’s Cycle:
10.6.9
Carnot’s Theorem:
10.6.10
Heat Pump and Refrigerator
10.6.10.1
Coefficient of Performance, COP:
10.6.11
Entropy
10.6.11.1
Principle of increase of entropy:
10.6.11.2
Principle of degradation of entropy:
10.6.12
Entropy and Probability
10.6.13
Third Law of Thermodynamics
10.7
Examples B
10.8
Exercise
Backmatter
A
(Mathematical Relations)
B
(Useful Data and Greek Letters)
C
List of Symbols
Index
References
Section
5.1
Work, Energy, and Power
If an object is displaced along the same direction as the force is applied then the
work
is said to be done. If a force
\(F\)
displaces a body to a distance
\(d\)
along the direction of force then work can be calculated by
\(W= Fd\text{.}\)
5.1.1
Work
5.1.2
Energy
5.1.3
Conservative and Non-Conservative Forces
5.1.4
Principle of Conservation of Energy
5.1.5
Energy Diagram
5.1.6
Loop-the-Loop Track
