Assistant Professor CHEW Lock Yue
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PAP 111: Mechanics and Relativity


Newton : If I can see further, it is because I stand on the shoulders of giants.
Einstein : Imagination is more important than knowledge.


Course Instructor

Assistant Professor CHEW Lock Yue
Emal: lockyue@ntu.edu.sg
Office: SBS B3 N-10
Tel: 6316-2968
webpage: http://www.ntu.edu.sg/home/lockyue/

Course Description

In this course, you will learn the simple and beautiful physical principles from these two giants of  physics who have revolutionized our world and have fundamentally changed our view on the fundamental quantities of nature.

The first part of this course introduces Newton’s mechanics. You will learn fundamental concepts such as Newton’s view on space and time, mass and force, the concept of energy, linear and angular momentum, and so on. These concepts are foundational, and they will be your companion as you journey into all areas of physics: quantum mechanics, electromagnetism, thermodynamics, statistical mechanics etc.

The second part of this course introduces you to the special theory of relativity of Albert Einstein. You will understand what Einstein’s mean when he says: “Pure thought can grasp reality”. By learning the relativistic mechanics due to Einstein’s, you will appreciate how his genius has fundamentally transformed our view of the fundamental quantities that we have introduced in the first part of the course: space and time, mass and energy, force and momentum.

We will end the course with a lecture on Universal Gravitation, a topic that is the culminating achievement of these two titans of physics. 

Course Meeting Time

Lectures: 33 sessions for 13 weeks. 1 hour per session. Monday 2:30pm to 4:30pm at NTU lecture theatre 11; and Friday 10:30am to 11:30am at NTU lecture theatre 9.

Tutorial: 6 sessions. Once every two weeks and held on the even week. 1 hour per session. Friday 10:30am to 11:30am at NTU lecture theatre 9.

Consultation

Appointment by Email.


Course Outline

  1. The Fundamental Quantities of Nature
  • Length, Time and Mass
  • Dimensional Analysis
  • Position, Velocity and Acceleration as Vector Quantities
  1. Galilean Theory of Relativity
  • The concept of reference frame
  • Relative Velocity in Reference Frames
  • Galilean Co-ordinate and Velocity Transformation
  1. Newton's Laws
  • The Concept of Force
  • Newton's First Law and Inertial Frames
  • Newton's Second Law
  • Newton's Third Law
  • Frictional and Resistive Forces
  • Non-Inertial Reference Frame - Centrifugal and Coriolis Forces
  1. Energy and Energy Transfer
  • The Concept of Work Done
  • Kinetic Energy and the Work-Kinetic Energy Theorem
  • Potential Energy and the Conservation of Mechanical Energy
  • Conservative and Non-conservative Forces
  1. Linear Momentum
  • The Conservation of Linear Momentum
  • Impulse and Momentum
  • The Collision Problem
  • Center of Mass and the Motion of a System of Particles
  • Rocket Propulsion
  1. Rotation Motion of a Rigid Object about a Fixed Axis
  • Angular Position, Velocity and Acceleration
  • Rotational Kinetics
  • Rotational Kinetic Energy
  • Mioments of Inertia
  • Torque and Angular Acceleration
  • Work, Power and Energy in Rotational Motion
  • Rolling Motion of a Rigid Object
  1. Angular Momentum
  • Angular Momentum and Torque
  • Angular Momentum of a Rotating Rigid Object
  • Conservation of Angular Momentum
  • The Motion of Gyroscopes and Tops
  1. Static Mechanics
  • The Conditions for Equilibrium
  • Center of Gravity
  • Examples of Rigid Objects in Static Equilibrium
  1. Einstein's Theory of Relativity
  • Electromagnetism and Newtonian Relativity
  • Location of the Absolute Frame and Michelson-Morley Experiment
  • The Postulates of Special Relativity Theory
  1. Consequences of Special Relativity
  • Simultaneity and the Relativity of Time
  • Time Dilation
  • The Twin Paradox
  • Length Contraction
  • Space-Time Graphs
  1. Relativistic Mechanics
  • The Lorentz Transformation Equations
  • The Lorentz Velocity Transformation Equations
  • The Relativistic Doppler Effect
  • Relativistic Linear Momentum
  • Relativistic Energy
  1. New Perspectives on the Fundamental Quantities of Nature
  • Mass and Energy
  • Space and Time, Momentum and Energy
  • Relativistic Form of Newton's Laws: Force and Momentum
  1. Epilogue: Newton and Einstein on Universal Gravitation
  • Kepler's Laws and the Motion of Planets
  • Newton's Law of Universal Gravitation
  • Einstein's General Theory of Relativity

Course Pre-requisites

Anyone who is familiar with elementary mechanics, elementary calculus, and a good knowledge of algebra will be able to follow the course.

Text

The following textbook is required or strongly recommended: You are expected to read through the relevant material before each lecture and complete a quiz in class.

Raymond A. Serway and John W. Jewett Jr., "Physics for Scientist and Engineers", Brooks/Cole - Thomson Learning, (2004).

The following text is supplemental to the topic of special relativity. You may want to look it up at the library.

Robert Resnick, "Introduction to Special Relativity", John Wiley and Sons, (1968).

Assignment

There will be six sets of tutorial problems. You will have two weeks to complete each assignment. Solutions will be available on the course site at Edventure the morning after the problem sets are due. Your solutions will be graded and returned during lecture as soon as possible.

Exams

  • A two hour mid-term assessment will cover materials through lecture 18.
  • A two and a half hour final examionation will cover materials from lecture 19 to lecture 33.


Grading

Problem sets and quizzes 10%, mid-term assessments 40%, final 50%.

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