Newtonian Mechanics of a Single Particle: Newton's Laws;
Reference Frames; Equation of Motion; Friction; Projectile Motion;
Statics; Linear and Angular Momentum; Energy; Conservation Theorems.
Newtonian Mechanics of a Single Particle: Newton's Laws;
Reference Frames; Equation of Motion; Friction; Projectile Motion;
Statics; Linear and Angular Momentum; Energy; Conservation Theorems.
Chapter 2.
Oscillations: Undamped and Damped Harmonic Oscillators in
One and two Dimensions; Phase Space and Phase Diagrams; Driven
Oscillators; Fourier Series.
Chapter 3.
Gravitation: Newton's Law of Gravitation; Potential;
Gauss's Law.
Chapter 5.
Central Force Motion: Two-Particles Problem Reduced to a
One-Particle Equivalent; Effective Potential; Planetary Motion and
Kepler's Laws; Orbits and Their Stability.
Chapter 8.
Systems of Particles: Center of Mass; Linear and Angular
Momentum of a System; Energy of a System; Elastic and Inelastic
Collisions of Two Particles.
Chapter 9.
Motion in a Noninertial Reference Frame:
Angular Velocity; Rotating Coordinate Systems; Centrifugal and
Coriolis Forces; Motion Relative to the Earth.
Chapter 10.
Dynamics of Rigid Bodies: Rotation about a fixed axis:
Moment of Inertia; Rotation about a moving axis: The Inertia Tensor;
Angular Momentum; Principal Axes of Inertia; Euler's Rigid Body
Equations.
Chapter 11.
| Date | Topics covered | Reference | 01/6 | Syllabus. Historical introduction to Classical Mechanics. and discussion of Newton's laws. | Sec. 2.1-2.3 | 01/8 | Brief review of elementary vector properties and notation. Derivative of a vector with respect to a scalar: position, velocity, and acceleration vectors. | Sec. 1.1,1.2,1.8-1.14 (not all) | 01/10 | From 2nd Newton's law: equation of motion, conservation of linear momentum. Integration of equation of motion to find velocity and position vectors. Introduction to Maple. | Sec. 2.4, First Maple tutorial (on this Web page) | 01/13 | Motion of a pointlike object under the action of a constant force: case of gravity on earth surface (projectile motion). | Example 2.6, see also second Maple tutorial (on this Web page). | 01/15 | Extension of the previous discussion to the case of systems of particles. Translational motion of single or systems of extended objects (block sliding down an incline, without/with friction, systems of block and pulleys, etc.). | Sec. 9.1-9.3, Examples 2.1-2.3,2.9 | 01/17 | Velocity dependent forces: retarding or dragging forces; horizontal and vertical motion of an object in the presence of a dragging force (and gravity). | Sec. 2.4, Examples 2.4,2.5 | 01/22 | Perturbative approach to the study of the motion of a projectile-like object in the presence of a velocity dependent dragging force. | Sec. 2.4 Example 2.7,2.8 | 01/24 | Discussion of Maple Tutorial n.3. Discussion of conservation theorems. Conservative forces and potential energy (one dimensional case). | Sec. 2.5 | 01/27 | Conservation of mechanical energy and qualitative study of physical systems moving under the influence of a given potential energy. | Sec. 2.6 | 01/29 | Study of the motion of a system in the vicinity of a stable equilibrium point: one dimensional case. Restoring forces and the motion of a one dimensional harmonic oscillator. | Sec. 2.6 (see also examples). Sec.3.1,3.2. Appendix C.1 | 01/31 | 2-dimensional harmonic oscillator. | Sec. 3.3 | 02/03 | Damped oscillations. Detailed discussion of the underdamped harmonic oscillator. | Sec. 3.5 | 02/05 | Detailed discussion of the overdamped and critically damped harmonic oscillator. Phase diagrams. | Sec. 3.5, 3.4 | 02/07 | Forced harmonic oscillator (with damping): solve the equation of motion for the case of a sinusoidal force. | Sec. 3.6. Appendix C.2 | 02/10 | Forced harmonic oscillator (with damping): resonance phenomena. Importance of studying the case of a sinusoidal force: Fourier theorem. | Sec. 3.6 | 02/12 | Discussion of Fourier Theorem. | Sec. 3.9 | 02/14 | Application of Fourier Theorem to specific examples. | Sec. 3.9 | 02/17 | Gravitational force, gravitational field, and gravitational potential. | Sec. 5.1-5.2 | 02/19 | Calculation of gravitational potential and gravitational field for an extended mass distribution: case of a uniform thin spherical shell. | Sec. 5.2+Notes available on demand. | 02/21 | First Midterm Exam. | Solutions available on the this Web page | 02/24 | Calculation of gravitational potential and gravitational field for a uniform spherical mass distribution (plus discussion of the case of a thick spherical shell). | Notes available on demand+Example 5.1 | 02/26 | Central forces: study of the two body problem. | Sec. 8.1-8.2 | 02/28 | Properties of the central-force motion. Review of kinematics using polar coordinates. | Sec. 8.3, Sec. 1.14 | 03/03 | Equations of motion for a central-force motion. Case of the gravitational force: solutions as conic sections. | Sec. 8.4 (notes available on demand) | 03/05 | Detailed study of elliptical conic sections. Interpretation of the results obtained for the reduced system: actual motion of the interacting masses, planetary motion and first Kepler's law. | Notes available on demand. | 03/07 | Second and third Kepler's laws. Introduction of the concept of effective potential, discussion of the effective potential for the gravitational force. | Secs. 8.7,8.6 | 03/17 | Direct integration of the motion in a gravitational field: relation between the parameters of the the orbit and energy and angular momentum of the motion. | Secs. 8.5,8.7 | 03/19 | Orbital dynamics. | Secs. 8.8 | 03/21 | Review of problems for Midterm n. 2. | Notes available on demand | 03/24 | Dynamics of system of many particles: center of mass and total linear momentum. | Secs. 9.1-9.3 | 03/26 | Dynamics of system of many particles: total angular momentum and mechanical energy. | Secs. 9.4-9.5 | 03/28 | Dynamics of systems of many particles: examples and problems. | Your notes! | 03/31 | Second Midterm Exam | Solutions available on the this Web page | 04/2 | Elastic/inelastic collisions: introduction | Secs. 9.6, 9.8 | 04/4 | Elastic collisions: Laboratory vs Center-of-Mass frame | Secs. 9.6,9.7 | 04/7 | Elastic collisions: Problems and Examples | Examples 9.7,9.8 + your notes | 04/9 | Rigid Body Motion: introduction, moment of inertia for rotation about a fixed axis. | Notes made available in class | 04/11 | Rigid Body Motion: calculation of moment of inertia for particular rigid bodies, parallel axis theorem. | Notes made available in class | 04/14 | Rigid Body Motion: examples and problems | Notes made available in class | 04/16 | Rigid Body Motion: examples and problems. | Notes made available in class | 04/18 | Motion in noninertial frames: rotating coordinate systems, noninertial forces. | Secs. 10.1-10.3 | 04/21 | Motion in noninertial frames: examples and problems. | Secs. 10.1-10.3 | 04/23 | Motion in noninertial frames: examples and problems, motion on earth surface. | Secs. 10.3-10.4 | 04/25 | Motion in noninertial frames: motion relative to earth surface. | Secs. 10.4 |