Measurements, Scalars and Vectors - Physics (Senior Secondary)

Physics starts with measurement. If you cannot measure it, you cannot understand how the physical world works. This course demystifies the foundation of physics by covering fundamental quantities, unit systems, and the crucial distinction between scalars and vectors. You will master the methods used to quantify reality and learn how to represent physical phenomena through precise mathematical language. Mastering these concepts is non-negotiable for anyone pursuing engineering, architecture, surveying, or any technical trade. You apply these principles whenever you calculate building structural loads, determine velocity for mechanical systems, or navigate across complex terrains. Understanding vectors allows you to predict the outcome of forces acting in different directions, a skill that transforms theoretical classroom knowledge into actionable problem-solving ability in the field. By the end of this course, you will demonstrate competence in identifying SI base units, performing accurate dimensional analysis, and applying the correct mathematical operations to scalar and vector quantities. You will accurately resolve vectors into components and compute resultants using graphical and analytical methods. You will gain the ability to choose appropriate measuring instruments for various physical tasks and interpret experimental data with high precision. This course targets senior secondary school students preparing for terminal examinations. However, it provides an essential bridge for university undergraduates in science or technical fields who need to reinforce their fundamental physics base. Even hobbyists or technical beginners will find this training invaluable for building a rigorous mental framework required for advanced scientific study and professional technical work.

$ 9.99

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.

Physics

Physics controls every machine, building, and system you will design or maintain. This complete programme covers every topic required for the JAMB UTME physics paper. You will move past basic definitions and learn to solve exact problems using standard laws and formulas. We focus strictly on measurements, mechanics, thermal properties, waves, electricity, and modern physics. You will gain a working knowledge of the physical world without unnecessary theory. This track suits senior secondary students preparing for WAEC, NECO, or JAMB examinations. It serves first-year university undergraduates in engineering or physical sciences who require a firm foundation. Technical beginners and independent learners who plan to enter engineering, medicine, telecommunications, or skilled trades will find these lessons essential for their next steps. You will finish able to calculate forces, analyse electrical circuits, predict wave behaviour, and explain atomic interactions. You will interpret laboratory data, apply mathematical models to physical systems, and answer examination questions with speed and accuracy. This preparation secures high scores in national entrance tests and builds the technical base required for university engineering degrees or direct entry into professional technical work.

Course Chapters

1. Introduction

This chapter establishes the foundational language of physics by introducing fundamental and derived physical quantities, their SI units, and the system of prefixes used for multiples and sub-multiples. You will learn how physical quantities are classified and how their units are constructed from base units. You will identify the seven fundamental quantities and their SI symbols; distinguish between fundamental and derived quantities; derive the units of common physical quantities such as area, volume, density, speed, force, energy and power; and apply standard SI prefixes from mega to pico.

Concept Overviews

5 Lessons

Problem Walkthroughs

8 Lessons

2. Dimensional Analysis

This chapter teaches you how to express any physical quantity in terms of the fundamental dimensions of mass, length and time. You will learn to use dimensional analysis as a tool for deriving units, verifying equations and checking the homogeneity of physical relationships. You will deduce the dimensional formulae of common physical quantities; verify the dimensional correctness of physical equations; determine the units of unknown constants in equations; and apply dimensional analysis to solve examination-style problems.

Concept Overviews

4 Lessons

Problem Walkthroughs

6 Lessons

3. Measurement of Length

This chapter covers the instruments and techniques used for measuring length with varying degrees of precision. You will learn to read vernier callipers and micrometer screw gauges, determine the least count and zero error of each instrument, and estimate the uncertainty in any measurement. You will take and record readings from a metre rule, vernier callipers and micrometer screw gauge; determine the least possible error of each instrument; correct for zero error; and calculate the possible error in derived quantities such as the thickness of a cylindrical vessel.

Concept Overviews

4 Lessons

Problem Walkthroughs

5 Lessons

4. Scalars and Vectors

This chapter introduces the critical distinction between scalar and vector quantities and teaches you how to represent vectors graphically. You will learn to classify physical quantities as scalars or vectors and understand why vector quantities require special methods of addition. You will classify common physical quantities as scalars or vectors; represent a vector quantity using a scaled line diagram; distinguish between distance and displacement; and specify position and direction using coordinate systems and cardinal points.

Concept Overviews

4 Lessons

Problem Walkthroughs

4 Lessons

5. Vector Addition (1)

This chapter teaches you how to find the resultant of two vectors using the parallelogram law and analytical methods. You will learn to combine vectors that are not in the same line and master the cosine and sine rules for calculating both magnitude and direction of the resultant. You will use scale drawings to apply the parallelogram law; calculate the resultant magnitude and direction using the cosine formula; resolve the special case of perpendicular vectors with Pythagoras' theorem; and determine the difference of two vectors by adding the negative.

Concept Overviews

3 Lessons

Problem Walkthroughs

3 Lessons

6. Vector Addition (2)

This chapter teaches you a simpler graphical method for adding two vectors — the triangle method — and applies vector addition to the practical problem of relative velocity. You will learn to draw vector triangles to scale and to solve for resultant displacements and velocities when a medium like a flowing river is involved. You will add two vectors by placing the tail of one at the tip of the other and drawing the resultant; use the triangle law to find resultants; solve for the resultant velocity of a boat crossing a river; and determine the direction in which a boat must head to reach a point directly opposite its starting point.

Concept Overviews

2 Lessons

Problem Walkthroughs

4 Lessons

7. Resolution of Vectors

This chapter teaches you how to replace a single vector with two perpendicular components and how to find the resultant of multiple vectors by resolving them into horizontal and vertical components. You will apply trigonometric functions to determine effective values of forces and velocities in specified directions. You will resolve a vector into horizontal and vertical components; calculate the effective horizontal or vertical component of a force or velocity; find the resultant of three or more coplanar forces by summing resolved components; and solve problems involving inclined planes and forces acting at angles.

Concept Overviews

4 Lessons

Problem Walkthroughs

4 Lessons

8. Conclusion

This chapter consolidates your understanding of measurements, units, scalars and vectors by reviewing the key concepts and problem-solving techniques covered throughout the course. You will revisit the classification of physical quantities, the reading of precision instruments, and the graphical and analytical methods of vector operations. You will review the SI system of units and dimensional analysis; practise reading vernier callipers and micrometer screw gauges; classify quantities as scalars or vectors; and solve comprehensive problems involving the addition and resolution of vectors.

Concept Overviews

1 Lesson