Applied Mathematics · Secondary 3

15/15 weeks ready · Follows the order of the Statics part of the Egyptian Ministry of Education and Technical Education textbook Applied Mathematics (Mechanics), Third Form Secondary (Grade 12), as the plan for Term 1 (the statics prerequisites on friction, then three units and five lessons: Moments, Coplanar forces, Couples; printed pages 2–57; the English and Arabic editions are the same book; the Dynamics part, printed pages 58–159, is not part of this plan). All explanations, exercises and quizzes are Darslab’s own.

Term 1Statics prerequisites: friction, the resultant reaction and the angle of friction, equilibrium on rough horizontal and inclined planes; Unit 1 Moments: the moment of a force about a point, Varignon’s principle and the theorem of moments; Unit 2 Coplanar forces: the resultant of parallel forces, equilibrium of a rigid body under coplanar forces (boards, rods, ladders); Unit 3 Couples: the couple and its moment, equivalent couples, a system equivalent to a couple and the resultant couple

Friction revisited: rough surfaces, μ and the angle of friction Statics prerequisites (Sec 2 friction revisited): smooth and rough surfaces, static friction and its limit, the coefficient of friction, kinetic friction, the resultant reaction and the angle of friction, equilibrium of a body on a rough horizontal plane and on a rough inclined plane

The moment of a force: turning effect, coordinates and Varignon Moments: the turning effect of a force about a point, moment arm and sign, the moment from coordinates, and Varignon’s principle

Theorem of moments, forces along rectangle sides, and two-point conclusions Moments: the theorem of moments for forces meeting at a point, forces along the sides of a rectangle or square, and equal or opposite moments about two points

Moments of any coplanar system, machines and mixed problems Moments: the general statement for a system of coplanar forces, moments in machines and mixed problems with unknowns

Parallel forces: like, unlike and the theorem of moments Parallel coplanar forces: the resultant of two like forces, of two unlike forces, and the theorem of moments for parallel forces

Several parallel forces and their resultant Parallel coplanar forces: an unknown force from the resultant, sums of moments of parallel forces, and the resultant of several parallel forces

Moving a force, forces as vectors and practice Parallel coplanar forces: moving one force, parallel forces given as vectors, and practice with resultants and balance points

The two conditions of equilibrium: boards, rods and strings Equilibrium of coplanar forces: the two conditions (zero resultant and zero moment), a board on two supports, and a rod on two strings

Non-uniform boards, loaded rods and a bar on a wedge Equilibrium of coplanar forces: a non-uniform board, rods and loads with unknown forces, and a bar on rough ground and a smooth wedge

Ladders and rods against a wall Equilibrium of coplanar forces: ladders on rough ground and a smooth wall, a ladder held by a rope, and a rod about to slip

Couples and their moments Couples: two equal opposite forces, the moment of a couple, its independence of the point, and equilibrium under several couples

Cancelling couples, hung bodies and equivalent couples Couples: cancelling a couple, a hanging body with a couple acting on it, equivalent couples and the exercises of Lesson 3-1

Systems equivalent to a couple Resultant couple: a system equivalent to a couple, forces along the sides of a triangle, and of a closed polygon

The three-point rule and resultant couples Resultant couple: the three-point rule, the sum of several couples, and the exercises of Lesson 3-2

Term 1 review: moments, parallel forces, equilibrium and couples Term 1 review: moments, parallel forces and equilibrium of rods and ladders, couples

The Egyptian Ministry of Education and Technical Education (MOETE) is not affiliated with, and does not endorse, Darslab. Lessons follow the order of the Ministry’s textbooks; all explanations, exercises and quizzes are Darslab’s own. Pictures of animals, plants and objects: Twemoji, CC BY 4.0.