Egypt (EN)

Egyptian National Curriculum - English

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Subjects

Applied Mathematics - Mechanics G12

  • Overview
  • Chapters

Applied Mathematics - Mechanics for 3rd year of secondary school

  • 1: Statics
    1.1: Friction
    1.1.1: The Equilibrium of a Body on a Rough Horizontal Plane
    1.1.2: Reaction
    1.1.3: Smooth and rough surfaces
    1.1.4: The properties of the static friction force
    1.1.5: kinetic friction force
    1.1.6: Resultant reaction
    1.1.7: Angle of friction
    1.1.8: The relation between coefficient of friction and angle of friction
    1.1.9: The Equilibrium of a Body on a Rough Inclined Plane
    1.2: Moments
    1.2.1: Moments in 2D
    1.2.2: The moment of a force about a point
    1.2.3: Algebraic measure of the moment
    1.2.4: The norm of the moment
    1.2.5: The moment of a force
    1.2.6: The magnitude of the moment measuring unit
    1.2.7: Principle of moments (Varignons theorem)
    1.2.8: General theorem of moments
    1.2.9: Moments in 3D
    1.2.10: Coordinate components of the moment of a force about a point
    1.3: Parallel Coplanar Forces
    1.3.1: Resultant of Parallel Forces
    1.3.2: Resultant of two Parallel Forces having the same directions (like forces)
    1.3.3: Resultant of two unlike Forces
    1.3.4: The resultant of a system of Parallel Forces
    1.3.5: Equilibrium of a Rigid Body under Parallel Forces
    1.4: General Equilibrium
    1.4.1: Equilibrium of a Rigid Body
    1.4.2: Vanishing of the moments of a set of forces about any point
    1.5: Couples
    1.5.1: Couple
    1.5.2: Moment of a Couple
    1.5.3: Equivalent of two couples
    1.5.4: Equilibrium of a Rigid Body under Coplanar Couples
    1.5.5: Equivalent System of Forces to a Couple
    1.5.6: Resultant couple
    1.6: Center of Gravity
    1.6.1: Center of Gravity of a rigid body
    1.6.2: The weight, center of gravity and gravitation of body
    1.6.3: The center of gravity of a system
    1.6.4: The center of gravity of two physical points
    1.6.5: Position vector of the center of gravity of a rigid body about the origin point
    1.6.6: The free suspension of a rigid body
    1.6.7: Center of Mass of Uniform Rods
    1.6.8: Center of Mass of Laminas
    1.6.9: The Negative Mass Method
    1.6.10: The center of gravity of some symmetric bodies
  • 2: Dynamics
    2.1: Rectilinear Motion
    2.1.1: Rectilinear Motion
    2.1.2: Position of the particle
    2.1.3: Displacement
    2.1.4: Velocity
    2.1.5: Acceleration
    2.1.6: The algebraic measure of the velocity vector and acceleration
    2.1.7: Linear Motion with Derivatives
    2.1.8: Applications of Derivatives on Rectilinear Motion
    2.1.9: Velocity–Time Graphs
    2.1.10: Definite integration
    2.1.11: Deducing the velocity and displacement
    2.1.12: Linear Motion with Integration
    2.2: Newton’s Laws of Motion
    2.2.1: Momentum
    2.2.2: Measuring units of momentum
    2.2.3: The change of momentum
    2.2.4: Newton’s First Law of Motion
    2.2.5: Inertia
    2.2.6: Force
    2.2.7: Newton’s Second Law: Constant Mass
    2.2.8: Newton’s Second Law: Variable Mass
    2.2.9: Newton’s Third Law of Motion
    2.2.10: Pressure and reaction
    2.2.11: Motion of a Body on a Smooth Inclined Plane
    2.2.12: Motion of a Body on a Rough Plane
    2.2.13: Applications of Newton’s Second Law: Two Masses Hanging from a Pulley
    2.2.14: Applications of Newton’s Second Law: Horizontal Pulley
    2.2.15: Applications of Newton’s Second Law: Inclined Pulley
    2.3: Impulse and Collision
    2.3.1: Impulse
    2.3.2: The measuring units of the magnitude of impulse
    2.3.3: Impulse and Momentum
    2.3.4: The impulsive forces
    2.3.5: Collisions and Conservation of Momentum
    2.3.6: Elastic collision
    2.3.7: Inelastic collision
    2.4: Work, Power & Energy
    2.4.1: Work Done by a Constant Force
    2.4.2: Work Done by a Force Expressed in Vector Notation
    2.4.3: Work and Integration
    2.4.4: Kinetic Energy
    2.4.5: The Work–Energy Principle
    2.4.6: Potential Energy
    2.4.7: Conservation of Energy
    2.4.8: Motion on a rough inclined plane
    2.4.9: Power
    2.4.10: Power as the Rate of Work

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