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PHYS 2P20
 Introductory Mechanics
Course outline
What Brock calendar entry says:
 Mechanics of particles and systems of particles by the Newtonian method; conservation of linear momentum, angular momentum and energy; elementary dynamics of rigid bodies; oscillators; motion under central forces; selected applications.
What do I need to bring into the course?
 This course is a core course of the Physics program, and requires Y1 Physics and Math courses as prerequisites.
Course Goals
 to develop a more comprehensive understanding of Newton's laws of motion and their origin in and application to real physical systems;
 to discover the underlying conservation laws and the manner in which physical systems evolve with time;
 to gain experience in the use of advanced mathematical tools (e.g. advanced algebra and trigonometry, analytic geometry, differential and integral calculus, differential equations);
 to develop experimental data analysis, error estimation, and numerical modelling skills;
 to enhance scientific writing skills.
Textbook
 An Introduction to Mechanics, second edition, by Daniel Kleppner and Robert Kolenkow. Cambridge University Press, 2013.
This is an approximate list, based on previous experience. As the course progresses, some of topics
may be removed and some others may get added.
 Vectors, a review of concepts
 algebra of vectors
 multiplication of two vectors: dot and crossproducts
 base vectors, orthonormality
 derivatives of vectors
 Kinematics in 2D and 3D
 elementary kinematics
 Ex: uniform circular motion
 solving kinematic equations
 2D motion in polar coordinates
 approximation methods: Taylor series and related expansions
 Newton's Laws
 Newton's Laws
 inertial and noninertial frames
 procedure for applying Newton's Laws to complex systems
 examples; constraints; nonphysical solutions
 linear restoring force
 momentum, impulse
 work and kinetic energy
 Harmonic oscillator
 potential energy, damping, formal solutions to the DE
 classification of solutions, under over and criticallydamped cases
 quality factor $Q$
 forced (driven) HO, resonance
 Ex: analogy with LCR circuits
 Kinematics in 3D
 work and energy in 3D, potentials, conservative forces
 momentum of a system of particles
 centerofmass, extended bodies, c.o.m. coordinates
 rocket motion
 momentum transport
 collisions between masses
 collisions and the c.o.m. coordinates
 Rotational motion and angular momentum
 angular momentum of a particle
 importance of the 3rd dimension: a conical pendulum
 conservation of angular momentum
 Ex: Kepler's 2nd law
 Ex: Bohr's atom, quantization of angular momentum
 Ex: torque on a conical pendulum
 angular momentum associated with a fixed axis' rotation
 moment of inertia
 parallel axis theorem
 solving problems involving torques
 the physical pendulum, center of gyration
 motions with both translation and rotation
 modified workenergy theorem
 generalization of rotational motion; infinitesimal rotations
 stability of rotating objects; a gyroscope
 generalization of angular momentum; tensor of inertia
Component 
% of the final mark 
Notes 
Homework 
20% 
Problem sets, every week. Late submissions have a sinking cap of 15%/day. 
Midterm test 
10% 
An inclass test, date TBA. Only a calculator and one lettersize (onesided) selfprepared formula sheet allowed; no complete solutions. 
Final exam 
35% 
Minimum passing grade 50%, marks given for correct answers. Only a calculator and one lettersize (onesided) selfprepared formula sheet allowed; no complete solutions. 
Labs 
35% 
Completion of all labs and submission of all lab reports is required to obtain a grade in the course. Late submissions will not be accepted. 
Here is a summary of our expectations of you, which are your responsibilities. You are expected to:
 attend each scheduled lecture and laboratory session;
 do your work honestly and maintain academic integrity (see a separate section below for details);
 complete each test, using only the materials that have been authorized for use, such as a nongraphics calculator and writing instruments;
 attend labs having prepared in advance by reading relevant parts of the lab manual, and having completed the prelab problems.
And most important of all, you must take responsibility for your own learning.
The lectures are there to guide you and assist you, but only you can actually do
the hard work of learning the course material. To get the most out of the
course, work on it a little bit every day. Daily work is key for placing your
learning in longterm memory, where it will be readily available to help you to
advance your knowledge in subsequent years  and acing the final exam, of
course. Cramming on the night before may place the material in your shortterm
memory and you might even do fine on a weekly test, where the amount of new
material is relatively small, but this approach will fail miserably on the
final exam.
Your instructor will provide weekly textbook chapter references; read through
those section. The best way is to read them twice: once before the lectures,
just to orient yourself in the material, to identify those parts that seem like
they might need extra time and attention. Make a note of the questions that
arise in your mind. The lecture should answer some of them, and if it does not,
raise your hand and ask! Asking questions is a sign of active learning, not a
sign of weakness. It is likely that many others have the same question. After
the lecture, read the textbook again, with a pen and paper in hand, repeating
all derivations on your own, trying every solved example before looking at the
solution, then solving every followup questions at the end of the section.
Sometimes, the answers to questions are available; use those to check up on the
skills you are developing. But most of the time, the answers are not known,
and you must learn to develop enough confidence in your skills to solve those.
Both are integral to the learning process.
Use your time effectively. Study smart, instead of hard. Ask questions in
class. Your instructor has an opendoor policy, so outside of a few restricted
hours, you are always welcome to come and ask a question oneonone. Do not
wait until you have a "worthy" pageful of questions  that's too long to let
them fester unanswered. It is better to come three times with one or two
questions than once with a list accumulated over the past several weeks, when
things get too desperate.
Please, note that while some of the chapterend problems will be assigned explicitly,
the students are encouraged and expected to review and attempt the majority of the chapterend problems in the book
for the readings assigned on a weekly basis.
All Textbook references are to
An Introduction to Mechanics, second edition, by Daniel Kleppner and Robert Kolenkow.
Cambridge University Press, 2013.

Before coming to class: review your Year 1 notes


Week 1. Vectors. Components of motion. Polar coordinates.


Week 2. Integration of kinematic equations.


Week 3. Newton's Laws.


Week 4. Momentum, work, energy

 K&K2, Ch.3.7
 K&K2, Ch.4.1;4.6.
 K&K2, Ch.5.15.3.1; 5.65.7; 6.16.3.

Week 5. A simple harmonic oscillator

Academic misconduct is a serious offence. The principle of academic integrity,
particularly of doing one’s own work, documenting properly (including use of
quotation marks, appropriate paraphrasing and referencing/citation),
collaborating appropriately, and avoiding misrepresentation, is a core principle
in university study. Students should consult
“Academic Misconduct” section in the Undergraduate Calendar
to view a fuller description of prohibited actions, and the procedures and penalties.
The University takes academic misconduct extremely seriously and will follow its
strict procedures to the letter in all cases.
A helpful website explains Brock's Academic Integrity Policy.
Please consult it, as all students are expected to know and abide by its provisions.
Courses may use turnitin.com , a phrasematching software, to verify originality
of your submitted lab reports and written assignments. If you object to uploading your assignmentsr
to turnitin.com for any reason, please notify the instructor to discuss alternative submissions.
Be aware that it is the policy of the Department of Physics that any academic
misconduct including (but not limited to) possessing, using or accessing
unauthorized material in any form (including online) during final exams or
assessments will automatically result in zero grade for the exam. Since
most courses require a minimum passing grade on the final exam to complete the
course, this will likely lead to a failure in the course.
FMS Penalties for Academic Misconduct
Unless otherwise specified, the Department of Physics follows the following
minimum penalty guidelines for cases of academic misconduct in the Faculty of
Mathematics and Science (FMS). Please be aware that the Associate Dean,
Undergraduate Programs, may assign different penalties than those listed here,
depending on the details of individual cases. Also note that cheating on exams
carries significantly higher penalties.
 First offence:
 Zero grade on the assignment, additional penalty of 100% of the weight of the
assignment to be subtracted from the final grade, mandatory completion of the
AZLS Academic Integrity workshop
 Second offence:
 Zero grade on assignment, additional penalty of 200% of the weight of the
assignment to be subtracted from the final grade, 4month suspension
 Third or additional offence:
 Zero grade in the course, 1year suspension, permanent removal from major program.
 Cheating on exams:
 Zero grade in the course, including for first offenses.
Intellectual Property Notice
All slides, presentations, handouts, tests, exams, and other course materials created by the instructor in this course are the intellectual property of the instructor. A student who publicly posts or sells an instructor’s work, without the instructor’s express consent, may be charged with misconduct under Brock’s Academic Integrity Policy and/or Code of Conduct, and may also face adverse legal consequences for infringement of intellectual property rights.
Use of Generative AI (GenAI)
In the age of GenAI (e.g., ChatGPT), our expectation of you remains the same as it ever was: original academic work, following the instructions of the assignment determined by the instructor for this course for requirements, expectations, and parameters for completion and submission of your work for grading. Therefore, the use of GenAI tools and GenAIgenerated content is not allowed (unless explicitly requested/instructed) as a resource or source for answers and discussion in submitted work. Unauthorized use of GenAI will be treated as an academic misconduct.
You probably won’t find much use of GenAI in this course anyway, even when writing something like a lab report. Why? GenAI doesn’t know what you did in the lab. GenAI may know a lot about the overall idea you were studying, but not how you demonstrated it. In your lab reports, your answers and discussion need to relate to what you did and the data you took.
Important dates
Please be aware of all the important dates, such as the first/last days of classes,
snow days and reading week, as well as the deadline for withdrawal without academic penalty.
For the current academic term, this information can be found here.
Relationship between attendance and grades
Unless the instructor announces otherwise, students are expected to attend all classes and labs and must submit all assignments in order to pass this course.
Accommodations
The University is committed to fostering an inclusive and supportive environment for all students and will adhere to the Human Rights principles that ensure respect for dignity, individualized accommodation, inclusion and full participation. The University provides a wide range of resources to assist students, as follows:

If you require academic accommodation because of a disability or an ongoing health or mental health condition, please contact Student Accessibility Services at askSAS@brocku.ca or 905 688 5550 ext. 3240.
 Medical SelfDeclaration Forms (brief absence up to 72 hours)
In the case of a shortterm medical circumstance, if a student wishes to seek an academic consideration, please use the Medical SelfDeclaration Form. The request is to be made in good faith by the student requesting the academic consideration due to a shortterm condition that impacts their academic activities (e.g., participation in academic classes, delay in assignments, etc.).
The period of this shortterm medical condition for academic consideration must fall within a 72hour (3 day) period. The form must be submitted to the instructor either during your brief absence or if you are too unwell, within 24 hours of the end of your 3 day brief absence.
Medical Verification Form (extended duration)
In cases where a student requests academic consideration due to a medical circumstance that exceeds 72 hours (three days) and will impact their academic activities (e.g., participation in academic classes, delay in assignments, etc.), or in the case of a final exam deferral, the medical verification form must be signed by the student and the health professional as per process set out in the Faculty Handbook III:9.4.1.

If you are experiencing mental health concerns, contact the Student Wellness and Accessibility Centre. Good2Talk is a service specifically for postsecondary students, available 24/7, 365 days a year, and provides anonymous assistance. Follow the above link or call 18669255454. For information on wellness, coping and resiliency, visit: Brock University (Mental Health).

If you require academic accommodation on religious grounds, you should make a formal, written request to your instructor(s) for alternative dates and/or means of satisfying requirements. Such requests should be made during the first two weeks of any given academic term, or as soon as possible after a need for accommodation is known to exist.

If you have been affected by sexual violence, the Human Rights & Equity Office offers support, information, reasonable accommodations, and resources through the Sexual Violence Support & Education Coordinator. For information on sexual violence, visit Brock's Sexual Assault and Harassment Policy or contact the Sexual Violence Support & Response Coordinator at humanrights@brocku.ca or 905 688 5550 ext. 4387.

If you have experienced discrimination or harassment on any of the above grounds, including racial, gender or other forms of discrimination, contact the Human Rights and Equity Office at humanrights@brocku.ca.
For a full description of academic policies in the Faculty of Mathematics and Science, consult brocku.ca/mathematicsscience/

