This course emphasizes a systematic approach to the mathematical formulation of mechanics problems and to the physical interpretation of the mathematical solutions. Topics covered include: Newton's laws of motion, kinematics and dynamics of a single particle, vector analysis, motion of particles, and gravitation. Recommended background: PH 1110, PH 1120, PH 1130, PH 1140, MA 1021, MA 1022, MA 1023, MA 1024 and concurrent registration in or completion of MA 2051. (The more important courses are in bold.)
The concepts of PH 1110 serve you very well for PH 2201. The
in this course are more challenging, however, and emphasis is placed on
your problem-solving skills and effective communication of your
solutions. PH 2201 problems tend to be very practically
you continue on to PH 2202, you will learn new, more theoretical
The text is "Newtonian Mechanics",
by A.P. French (ISBN-13: 978-0-393-09970-6),
available in the bookstore. Clickers may be borrowed from ATC, to
the right of the Helpdesk in the Gordon Library. Beware that
failure to return them at the end of the term will result in a $75
charge to your account.
We meet in OH 223 on MTThF at 11:00. Instructor: Professor NA Burnham, email@example.com.
||The three exams. 10%
penalty for make-ups.
| 30 %
||The ten highest scores of the twelve homework assignments. No late work accepted.|
||Answers to clicker questions during class. You earn one point for answering and two points for answering correctly. Four lowest daily scores dropped; make-ups are not possible. Proper operation of your clicker is your responsibility. You may borrow a clicker from ATC. Failure to return it at the end of the term results in a $75 charge to your account.|
Chapters 4, 7
Chapters 9, 10
Chapters 8, 11, 13
||Summary and problems
pp. 3-12; do Problems 4-1 (Include clear free-body, or "isolation",
diagrams in your argument. Can a real rope ever be perfectly horizontal
its entire length? Explain your answer, with the help of a free-body
diagram.), 4-3, 4-6, 4-14.
|HW2||Summarize pp. 33-38, 74-78; do Problems 7-4, 7-6 (Symbolically only; clearly define your variables.), 7-18, 7-21 a & b only.|
pp. 139-154. Two of these problems are numerical. Remember
to do symbolic solutions first: Problems 7-23, 7-24, 7-26.
You may estimate the second part of 7-26 by justifying with a sketch
showing v(t) with and without air. The fourth problem concerns a
sphere of uniform density falling in a constant gravitational
field. The air resistance is c_1 rv + c_2 r^2v^2. Find the
terminal speed as a function of radius r. Show that your result
is dimensionally correct. Take the limits r -> 0, r ->
small, r -> big. Show with free-body diagrams that your last
correspond to the cases of linear and quadratic resistance.
pp. 161-173; do Problems 7-29, 7-30, 7-31, 7-32.
|HW5||Summarize pp. 307-320; do Problems 9-1, 9-4, 9-5, 9-6. Problem 9-6 may be done numerically, but show a sketch of what's happening for each step. The requested plot is not necessary.|
pp. 321-335; do Problems 9-10, 9-11, 9-12 a-c, 9-12 d-f.
pp. 367-384; do Problems 10-12, 10-13 a-d, 10-15 (Show that with the
limit of k_2/k_1 small, you get what you expect for a spring force of
pp. 393-411; do Problems 10-19, 10-24 (Find the three x(b) values for
which E = U in part e. You may use Maple or Wolfram. How
are they the same or different from part e?), 10-26, 10-33.
pp. 245-259; do Problems 8-3, 8-15, 8-17, 8-20.
pp. 259-274; do Problems 11-17, 11-18, 11-21, 11-23.
pp. 274-286; do Problems 13-3, 13-4, 13-6, and similarly to 13-9,
sketch two effective potential diagrams. On the first, show the initial
circular orbit and the subsequent orbits if the rocket is fired towards
or away from the Earth. On the second, again show the initial circular
orbit and the two subsequent orbits if the rocket is fired to give the
satellite more and less tangential speed.
pp. 286-300; do Problems 13-12, 13-16, 13-19a, 13-22.
Mechanics is the study of motion. Its history dates from Galileo and Newton and was developed further by Lagrange and Hamilton. About a hundred years ago, scientists started to develop relativistic mechanics and quantum mechanics, and to distinguish among them, the traditional form of mechanics has become known as "Classical Mechanics."
Newton's famed three laws of motion are based upon ideas that concern space, time, mass, and force. Space can be described by coordinate systems, the simplest one being the cartesian coordinate system, which has three orthogonal axes. The position of an object can be determined by a position vector, and the next few pages of the text reviews vector algebra. After further reminders of time, reference frames, mass, and force, Newton's laws are introduced.
The First Law says that a particle moves with a constant velocity unless acted upon by an external force. The Second Law states the relationship between mass, a scalar, and acceleration, a vector. Their product equals the vector sum of all the forces acting on a particle. Since acceleration is the second derivative of position with respect to time, the Second Law is a differential equation. Newton's Laws hold in what are called inertial reference frames. They do not always hold for relativistic or quantum systems. Nonetheless, they are valid over a wide range of scales in size and speed and are thus worthy of study.
The Third Law states the relationship between "action" forces and "reaction" forces. They are equal in magnitude and opposite in direction, but act on two different bodies. From the Third Law, which considers only one particle, one can construct a theory for many particles. Internal forces in a multiparticle system have no influence on the total momentum. In other words, if the external forces are constant, then momentum is conserved. Taylor gives an example where, apparently, the Third Law is violated, but then explains that mechanical momentum is not the only form of momentum. It can, for example, be electromagnetic. However, Taylor assures us that for the rest of his text, we will consider situations only in which the Third Law holds.
|Points||For each problem (out of five possible points):|
|-5||No symbolic solutions|
||Symbolic solution has wrong dimensions|
|-1 to -5||Write-up hard to read or understand|
|-1||Vectors confused with scalars or vice versa|
||Missing or incorrect units on
|-1||No boxes around symbolic and numerical answers
|For the summaries (out of five possible points):|
||Equations in summary|
|-1 to -5
||Symbols in summary|
|-1 to -5
||Not enough detail|
||Shorter or longer than specified length, in increments of 50 words|
||No word count|
|In general, for any given problem or summary:|
|5 =||Excellent -- write-up clear and correct|
|4 =||Good -- write-up clear and mostly correct, or understandable
|3 =||Acceptable -- write-up understandable and mostly correct, or
poor write-up and correct, or clear write-up and incorrect
|And for an entire assignment:|
|Top of this page|
|WPI Department of Physics Home page|
|WPI Home page|