Last updated: April 25, 2006

Mechanics (Fy2010/L) Course Information

Text Book

Main course book: An Introduction to Mechanics, by Daniel Kleppner and Robert J. Kolenkow, McGraw-Hill International Editions (Sections of the book that are part of the course are indicated below)

Supplementary text book for additional reading: Classical Mechanics, by John R. Taylor

Old Examinations

Two recent solved exams are: May 2005 , Aug 2005 . Two earlier examination papers are found here . (Copies of still older exams with solutions have been distributed in the class. If you have not got one, please contact me).

Suggested Problems

Suggested problems from the book and from the yellow "Övnningsproblem i mekanik" can be found
here (Consider only chapters that have been covered in this course and note that the description in line 2 and 3 does not apply to this course)

Homework Problems

Homework problem set I
pdf file (Due date: May 2, 2006)

Course Content

Chapter 1: Vectors and Kinematics
    Topics Covered:
  • Vectors, addition of vectors, unit vectors, components of a vector (in Cartesian coordinates), Scalar (dot) product and vector (cross) product of two vectors.
  • Basic description of motion: position vector, displacement, velocity, momentum, acceleration, description of motion with constant acceleration.
  • Uniform circular motion (angular velocity and radial acceleration), polar coordinates in 2 dimensions, general 2-dimensional motion in polar coordinates, radial and angular components of velocity and acceleration.
    Relevant Sections in the Book: 1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.9 (important, upto page 37)

Chapter 2: Newton's Laws of Motion
    Topics Covered:
  • The need for reference frames, Newton's first law of motion, the concept of inertial and non-inertial reference frames, isolated bodies.
  • Newton's second law of motion, unit of force, principle of superposition, interaction as the origin of force, non-inertial frames and the concept of fictitious forces.
  • Newton's third law of motion, action and reaction
  • Some common examples of force: Newton's law of gravitation, gravity due to empty and solid spherical shells (no derivations), weight, acceleration due to gravity.
  • Linear restoring force (Hooke's law), Motion under a linear restoring force (Simple Harmonic Motion): general solution of the simple harmonic equation, the concept of initial conditions, time period and frequency of the oscillations.
  • Contact forces: tension on a string, normal force (perpendicular to a surface), friction
    Relevant Sections in the Book: 2.1, 2.2, 2.4, 2.5 (topics on pulleys and viscocity not included)
    Relevant Examples: 2.3, 2.5, 2.6, 2.8, 2.10, 2.11, 2.12, 2.17, 2.18

Chapter 3: Momentum
    Topics Covered:
  • Newton's second law in terms of momentum, Dynamics of a system of particles: total momentum and total external force, center of mass, motion of center of mass, conservation of momentum and its importance, impulse and the significance of interaction time.
    Relevant Sections in the Book: 3.1, 3.2, 3.3, 3.4
    Relevant Examples: 3.2, 3.6, 3.8 (no need to use the CoM coordinates), 3.10

Chapter 4: Work and Energy
    Topics Covered:
  • Work, Integrating the equation of motion in 1 dimension, Work-Energy theorem in 1 dim, Calculation of work for some forces: a) uniform gravitational field, b) linear restoring force, c) inverse square force (escape velocity)
  • Integrating equation of motion in 3 dimensions, Work-Energy theorem, Work done by uniform and central forces, Conservative forces and potential energy, Total mechanical energy and its conservation, Potential in a uniform gravitational field, harmonic oscillator potential, gravitational potential, Shape of potential energy curve and stability.
    Relevant Sections in the Book: 4.1, 4.2, 4.3, 4.4, 4.5, 4.7, 4.8, (recommended reading: 4.9, 4.10)
    Relevant Examples: 4.1, 4.2, 4.3, 4.4, 4.5, 4.7, 4.8, 4.11, 4.12, 4.13,

Chapter 6: Angular Momentum and Fixed Axis Rotation
    Topics Covered:
  • Angular momentum of a particle, Torque and the conservation of angular momentum, Central force motion and Kepler's law of equal areas, Angular momentum of an extended body and moment of inertia, Calculation of moment of inertia in some simple cases, The parallel axis theorem, Dynamics of pure rotation about an axis, kinetic energy of a rotating body, axis of gyration, The physical pendulum
  • Motion Involving Both Translations and Rotations, analysis for angular momentum, torque and kinetic energy.
    Relevant Sections in the Book: 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7
    Relevant Examples: 6.1, 6.2, 6.3, 6.5, 6.6, 6.7, 6.8, 6.9, 6.10, 6.14, 6.15, 6.16, 6.17

Chapter 8: Non-inertial Systems and Fictitious Forces
    Topics covered:
  • Transformations between reference frames, Galilean transformations and inertial frames, Uniformly accelerated systems and the equivalence principle, Physics in rotating coordinate systems, centrifugal and Coriolis forces, The case of the rotating earth, Foucault's pendulum
    Relevant Sections in the Book: 8.1, 8.2, 8.3, 8.4, 8.5
    Relevant Examples: 8.1, 8.2, 8.3, 8.6, 8.7, 8.8, 8.9, 8.11,

Chapter 10: The Harmonic Oscillator
    Topics covered:
  • Review of simple harmonic motion, Damped harmonic oscillator, Forced harmonic oscillator, Forced damped harmonic oscillator, resonance and energy considerations
    Relevant Sections in the Book: 10.1, 10.2 (leave out the Q-factor), 10.3, 10.4
    Relevant Examples: 10.1, 10.3, 10.4, 10.5,

Chapter 11: The Special Theory of Relativity
    Topics covered:
  • Galilean transformations and Galilean addition of velocities, Qualitative description of inconsistency with experiments and with the theory of electromagnetism (constancy of the speed of light), The postulates of Special Relativity, Derivation of Lorentz transformations.
    Relevant Sections in the Book: 11.1, 11.3,
    Relevant Examples: 11.1, 11.2

Chapter 12: Relativistic Kinematics
    Topics covered:
  • Implications of Lorentz Tansformations: observer dependence of simultaneity, Lorentz contraction, Time dilation, Relativistic transformation of velocity.
    Relevant Sections in the Book: 12.1, 12.2, 12.3, 12.4
    Relevant Examples: 12.1, 12.2, 12.3, 12.4, 12.5, 12.6, 12.7

Chapter 13: Relativistic Momentum and Energy
    Topics covered:
  • Relativistic momentum and its conservation, the concept of velocity dependent mass, Relativistic kinetic energy,Total energy and mass-energy equivalence, energy-momentum relationship, the notion of massless particles.
    Relevant Sections in the Book: 13.1, 13.2, 13.3
    Relevant Examples: 13.2, 13.3, 13.5

Space-time Intervals and Diagrams
    Topics covered:
  • Space intervals, Time intervals and Space-time intervals, Invariance of space-time intervals under Lorentz transformations, Types of Space-time intervals: space-like, time-like and light-like, The notion of causality and its invariance under Lorentz transformations, Space-time interval as a distance between two events in Minkowski space.
  • Space-time diagrams, the light-cone and causality