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Home > Courses > 2P20
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PHYS 2P20
- Introductory Mechanics
- The final exam is scheduled for December 19, 2023, 19:00-22:00.
These are previously made announcements:
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.
| 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 in-class test, date TBA. Only a calculator and one letter-size (one-sided) self-prepared formula sheet allowed; no complete solutions. |
| Final exam |
35% |
Minimum passing grade 50%, marks given for correct answers. Only a calculator and one letter-size (one-sided) self-prepared 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. |
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 cross-products
- 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 non-inertial frames
- procedure for applying Newton's Laws to complex systems
- examples; constraints; non-physical 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 critically-damped 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
- center-of-mass, 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 work-energy theorem
- generalization of rotational motion; infinitesimal rotations
- stability of rotating objects; a gyroscope
- generalization of angular momentum; tensor of inertia
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