WAYLAND BAPTIST UNIVERSITY
DIVISION OF MATHEMATICS & SCIENCES
COURSE NO. AND TITLE:
MATH 3303 – Vector Mechanics
Description: This course develops skills in vector algebra, components of vector forces,
equilibrium, moments, couples, free-body diagrams, centroids, and analysis of structure.
This course is designed primarily for pre-engineering students
Text: Vector Mechanics for Engineers: Statics, 7th Ed., by Beer, Johnston and Eisenberg
(McGraw Hill)
Supplies: All students need to have a scientific calculator that has at least log x, ln x, and
the exponential functions. (I recommend the TI-83, TI-86 or TI-89).
Prerequisites: MATH 3300 or division approval
Class Policies:
Attendance:
All students are expected to attend all class sessions and are responsible
for knowing the material covered. No quizzes or exams can be made up unless
arrangements PRIOR to the absence have been made. Any student missing more than 25%
of the class will FAIL the class.
Academic Honesty: Disciplinary action for academic misconduct is the responsibility of
the faculty member assigned to this course. The faculty member is charged with assessing
the gravity of any case of academic dishonesty, and with giving sanctions to any student
involved.
Student Expectations - suggested
Homework: Homework will be assigned at the end of each section in the text and will
generally be due one week from the date of assignment. All assignments will be posted to
the website, along with due date. Late homework will NOT be accepted. All homework is
graded on a 50 point scale (from 50 to 100). You will receive 50 points for handing in a
COMPLETE ASSIGNMENT. This means at least 80% of the problems attempted and you
MUST show your work. (Note that an assignment with only the answers will be considered
incomplete and you will receive no credit for that assignment.)
Exams: During the semester there will be 4 exams. The content covered by each exam
will be explicitly discussed in class. The class period prior to each exam will include a
review. At the close of the semester, the lowest exam grade is dropped.
Final: The Final Exam will be comprehensive. All students will be required to take the Final
Exam
Grading - suggested
30%
40%
30%
Homework
Exams
Final
A: 90 – 100
B: 80 – 89
C: 70 – 79
D: 60 – 69
F: Below 60
Outcome Competencies:
Be able to discuss and work problems in the following areas:
Vectors
Forces
Systems of Forces and Moments
Objects in Equilibrium
Structures in Equilibrium
Centroids and Centers of Mass
Moments
Analysis of Simple Trusses
Complete a project that shows competence in this type of mathematical
engineering.
Course Outline:
Introduction
What is Mechanics?
Fundamental concepts and principles
Systems of Units
Conversion from one system of units to another
Method of problem solution
Numerical accuracy
Statics of Particles
Forces in a Plane
Force on a particle. Resultant of two forces
Vectors
Addition of vectors
Resultant of several concurrent forces
Resolution of a force into components
Rectangular components of a force. Unit vectors
Addition of forces by summing x and y components
Equilibrium of a particle
Newton’s first law of motion
Problems involving the equilibrium of a particle. Free-body diagrams
Forces in Space
Rectangular components of a force in space
Force defined by its magnitude and two points on its line of action
Addition of concurrent forces in space
Equilibrium of a particle in space
Rigid Bodies: Equivalent Systems of Forces
External and internal forces
Principle of transmissibility. Equivalent forces
Vector product of two vectors
Vector products expressed in terms of rectangular components
Moment of a force about a point
Varignon’s Theorem
Rectangular components of the moment of a force
Scalar product of two vectors
Mixed triple product of three vectors
Moment of a force about a given axis
Moment of a couple
Equivalent couples
Addition of couples
Couples can be represented by vectors
Resolution of a given force into a force at O and a couple
Reduction of a system of forces to one force and one couple
Equivalent systems of forces
Equipollent systems of vectors
Further reduction of a system of forces
Equilibrium of Rigid Bodies
Free-body diagrams
Equilibrium in two dimensions
Reactions at supports and connections for a two-dimensional structure
Equilibrium of a rigid body in two dimensions
Statically indeterminate reactions. Partial constraints
Equilibrium of a two-force body
Equilibrium of a three-force body
Equilibrium in three dimensions
Equilibrium of a rigid body in three dimensions
Reactions at supports and connections for a three-dimensional structure
Distributed Forces: Centroids and Centers of Gravity
Areas and Lines
Center of gravity of a two-dimensional body
Centroids of areas and lines
First moments of areas and lines
Composite plates and wires
Determination of centroids by integration
Theorems of Pappus-Guildinus
Volumes
Center of gravity of a three-dimensional body. Centroid of a volume
Composite bodies
Analysis of Structures
Trusses
Definition of a truss
Simple trusses
Analysis of trusses by the Method of Joints
Analysis of trusses by the Method of Sections
It is the university policy that no otherwise qualified disabled person be excluded from
participation in, be denied the benefits of, or be subject to discrimination under any
educational program or activity in the University. Students should inform the instructor of
existing disabilities at the first class meeting.
This syllabus is only a plan. The teacher may modify the plan during the course. The
requirements and grading criteria may be changed during the course if necessary.
rev. 11/05