Introduction to Vector Mechanics - Vectors (Undergraduate Foundation)

This course provides a rigorous introduction to classical mechanics using the language of vectors. We cover the two main branches of the subject: dynamics, where you will analyze forces, equilibrium, work, energy, and moments; and kinematics, where you will describe the motion of particles using position, velocity, and acceleration. You will learn to analyze a wide range of scenarios, including projectile and circular motion. Mechanics is the science of how things move and interact, forming the foundation of all physical sciences and engineering. This course is designed to build your problem-solving intuition by applying vector principles to tangible, real-world scenarios. You will learn to model physical systems mathematically, providing a powerful framework for understanding the world around you. This programme is designed for students who have completed our introductory course on vector calculus. It is the ideal next step for first-year university students in physics, engineering, and other physical sciences. This course provides the essential foundation required before tackling more comprehensive topics in the main Engineering Mechanics learning track.

Payment required for enrolment
Enrolment valid for 12 months
This course is also part of the following learning track. You may join the track to gain comprehensive knowledge across related courses.
[OAU, Ife] MTH 104: Vectors
[OAU, Ife] MTH 104: Vectors
This comprehensive learning track guides you through the complete world of vector analysis. We begin with the fundamentals of vector algebra and its application to foundational geometry. You will then master scalar, vector, and triple products before using them to construct the vector equations of lines, planes, and conics. The journey culminates in advanced topics, including vector calculus, its applications in classical mechanics, and an introduction to differential geometry. Vectors are the essential language used to describe our physical world, making their mastery non-negotiable for any serious student of science or engineering. This track is designed to build your intuition for spatial reasoning and equip you with a powerful problem-solving toolkit. You will see direct applications in mechanics, analyzing forces and motion; in geometry, calculating angles and distances; and in calculus, modeling dynamic change over time. While this track is tailored to the first-year university curriculum for MTH 104 at Obafemi Awolowo University, Ile-Ife, Nigeria, it is an invaluable resource for a wide range of learners. It is ideal for any undergraduate student in mathematics, physics, engineering, or computer science seeking a comprehensive understanding of vector analysis. Furthermore, it serves as an excellent and thorough refresher for professionals who wish to solidify their foundational knowledge of this critical subject.

This comprehensive learning track guides you through the complete world of vector analysis. We begin with the fundamentals of vector algebra and its application to foundational geometry. You will then master scalar, vector, and triple products before using them to construct the vector equations of lines, planes, and conics. The journey culminates in advanced topics, including vector calculus, its applications in classical mechanics, and an introduction to differential geometry. Vectors are the essential language used to describe our physical world, making their mastery non-negotiable for any serious student of science or engineering. This track is designed to build your intuition for spatial reasoning and equip you with a powerful problem-solving toolkit. You will see direct applications in mechanics, analyzing forces and motion; in geometry, calculating angles and distances; and in calculus, modeling dynamic change over time. While this track is tailored to the first-year university curriculum for MTH 104 at Obafemi Awolowo University, Ile-Ife, Nigeria, it is an invaluable resource for a wide range of learners. It is ideal for any undergraduate student in mathematics, physics, engineering, or computer science seeking a comprehensive understanding of vector analysis. Furthermore, it serves as an excellent and thorough refresher for professionals who wish to solidify their foundational knowledge of this critical subject.

Course Chapters

1
Introduction

Welcome and outline of course.

Chapter lessons

1.Welcome

Welcome to the course and outline of course.

2
Mechanics I

An introduction to applications of vectors in mechanics - forces and their resultants; equilibrium under the action of concurrent forces; work done by constant and variable forces; kinetic and potential energy; conservation of energy principle; moment of a force about a point.

Chapter lessons

1.Concurrent forces

The resultant of two or more forces acting at a point; equilibrium of a particle under the action of forces.

2.Work

Re-examining the work done by constant forces and variable forces.

3.Energy

Kinetic and potential energy; power; conservation of mechanical energy.

4.Moments

Moment of a force.

5.Worked examples (1)

Worked examples involving concurrent forces, equilibrium, work, energy, power, and moments of forces.

6.Worked examples (2)

More worked examples involving concurrent forces, equilibrium, work, energy, power, and moments of forces.

7.Worked examples (3)

More worked examples involving concurrent forces, equilibrium, work, energy, power, and moments of forces.

8.Worked examples (4)

More worked examples involving concurrent forces, equilibrium, work, energy, power, and moments of forces.

3
Mechanics II

An introduction to applications of vectors in mechanics - displacements, velocities and accelerations; relative velocities and accelerations; motion of a particle in tangential and normal components; motion of a particle in radial and transverse components (polar coordinates).

Chapter lessons

1.Velocity and acceleration

Relations between the position, distance, displacement, speed, velocity and acceleration of a particle.

2.Relative velocity and acceleration

Meaning and measurement of relative position, velocity and acceleration.

3.Normal and tangential components

Defining the curvilinear motion of a particle using normal and tangential vectors.

4.Radial and transverse components

Defining the curvilinear motion of a partial using radial and transverse components.

5.Worked examples (1)

Worked examples on vector analysis of rectilinear and curvilinear particle motions.

6.Worked examples (2)

More worked examples on vector analysis of rectilinear and curvilinear particle motions.

7.Worked examples (3)

More worked examples on vector analysis of rectilinear and curvilinear particle motions.

4
Mechanics III

An introduction to the applications of vectors in mechanics - motion of a particle along a path of constant radius; motion of a particle in cylindrical coordinates; motion in rotating and fixed frames.

Chapter lessons

1.Constant radius

Vector analysis of the motion of a particle along a path of constant radius.

2.Cylindrical coordinates

Vector analysis of the motion of a particle using cylindrical coordinates.

3.Rotating frames

Vector analysis of the motion of a particle relative to a rotating frame of reference..

4.Worked examples (1)

Worked examples on the vector analysis of the motion of a particle involving a path of constant radius, cylindrical coordinates or rotating frames.

5.Worked examples (2)

More worked examples on the vector analysis of the motion of a particle involving a path of constant radius, cylindrical coordinates or rotating frames.