Introduction to engineering mechanics, fundamental concepts, systems of units and general analysis procedure.

Fundamental concepts (3)

Fundamental concepts (4)

Conversion from one system of unit to another.

Systems of units (2)

Meaning of mechanics and engineering mechanics.

Mechanics

The parallelogram law of addition of forces and the principle of transmissibility of forces.

Fundamental concepts (2)

Meaning of particles and rigid bodies in the context of engineering mechanics.

Particles and rigid bodies

Meaning of rigid-body mechanics and its branches - statics and dynamics.

Rigid-body mechanics

Welcome

Fundamental concepts (1)

Units of measurement of mass, length, time, force, etc., in the S. I. and U. S. customary units.

Systems of units (1)

General procedure for solving engineering mechanics problems.

General procedure

Introduction

Force vectors and how to obtain the resultant of two or more forces - using parallelogram and triangle rules.

Representation of forces using directed line segments.

Force vectors

Worked examples on resultant of forces in two dimensions.

Worked examples (1)

More worked examples on resultant of forces in two dimensions.

Worked examples (2)

Worked examples (5)

Addition of several concurrent forces by successive applications of the parallelogram / triangle rule.

Several concurrent forces

Addition of force vectors using the parallelogram rule.

Parallelogram rule

Addition of force vectors using the triangle rule.

Triangle rule

Worked examples (9)

Worked examples (6)

Worked examples (7)

Worked examples (10)

Worked examples (4)

Worked examples (3)

Worked examples (8)

Resultant of Forces in a Plane

Resolution of a force into its rectangular and non-rectangular components.

More worked examples on calculating the components of a force.

Meaning of rectangular components of a force.

Rectangular components

Worked examples on calculating the components of a force.

Meaning of components of a force, in general.

Components

Components of a Force in a Plane

Calculating the resultant of several concurrent forces using their rectangular components.

More worked examples on calculating the resultant of several concurrent forces by resolution of each force into rectangular components.

How to find the resultant of several concurrent forces by resolution of each force into rectangular components.

Procedure

Worked examples on calculating the resultant of several concurrent forces by resolution of each force into rectangular components.

Resultant by Components in a Plane

Equilibrium of particles under the action of planar forces.

Condition for equilibrium of a particle in two dimensions.

Condition

More worked examples on the equilibrium of a particle in two dimensions.

Equations and procedure for analysis of equilibrium of a particle in two dimensions.

Worked examples on the equilibrium of a particle in two dimensions.

Worked examples (11)

Worked examples (12)

Worked examples (13)

Equilibrium in a Plane

Determining the components of forces in three dimensions.

Worked examples on resolution of a force in three dimensions into its components.

How to obtain the components of a force in three dimensions using its magnitude and coordinates of any two distinct points along its line of action.

Magnitude and two points

More worked examples on resolution of a force in three dimensions into its components.

How to obtain the components of a force in three dimensions from its magnitude and two angles defining its orientation.

Magnitude and two angles

Review of the scalar or dot product of two vectors; how to obtain the projection (component) of a force to a given direction.

Projections

An illustration of the rectangular components of a force and its direction cosines in three dimensions.

Worked examples (15)

Worked examples (17)

Worked examples (16)

Worked examples (14)

Worked examples (18)

Components of a Force in Space

Vector addition of force vectors in three dimensions.

More worked examples on addition of vectors in three dimensions.

Procedure for summing force vectors in three dimensions.

Worked examples on addition of vectors in three dimensions.

Resultant of Forces in Space

Equilibrium of particles under the action of three-dimensional forces.

Worked examples on equilibrium of a particle in three dimensions.

More worked examples on equilibrium of a particle in three dimensions.

Condition for equilibrium of a particle in three dimensions.

Equilibrium in Space

Analysis of systems of concurrent forces in two and three dimensions; equilibrium of particles in two and three dimensions.

Tutorials for undergraduates in engineering and physical sciences.

Statics of Particles - Engineering Mechanics (Statics)

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