Applied Mathematics 1B

About Course

Welcome to Applied Mathematics 1B, a foundational course designed to equip you with the essential principles of mechanics. This course delves into the analysis of forces and motion, providing the mathematical tools necessary to solve real-world engineering problems. You will explore the core concepts of statics and dynamics, learning how to analyze systems at rest and in motion, from simple particles to complex rigid bodies.

Analyze Particle Motion: Describe and solve problems involving the motion of particles along straight and curved paths using Cartesian, normal-tangential, and polar coordinate systems.
Determine Geometric Properties: Calculate centroids of areas, volumes, and lines, as well as the center of mass for composite objects.
Understand Rotational Effects: Calculate moments of inertia for various shapes and apply the parallel axis theorem to solve complex problems.
Solve Friction Problems: Analyze and determine the effects of static and kinetic friction in mechanical systems.
Apply Newton's Laws: Utilize Newton's second law to analyze the kinetics of particles in different coordinate systems.
Use Work-Energy and Impulse-Momentum Methods: Apply the principles of work, energy, impulse, and momentum to solve for the motion of particles and rigid bodies.
Master Rigid Body Dynamics: Investigate the planar kinematics and kinetics of rigid bodies, including the principles of work and energy.

Course Content

Friction

Motion Of Particles In Straight Line

Curvilinear Motion Of Particles In Cartesian Coordinate System

Curvilinear Motion Of Particles In Normal-Tangential Coordinates

Curvilinear Motion Of Particles In Polar Coordinates

Centroids Of Areas And Composite Areas

Centroids Of Volumes And Lines

Centre Of Mass Of Objects

Moments Of Inertia

Parallel Axis Theorem For Areas

Moment of Inertia For Simple Objects

Newton’s Second Law In Cartesian Coordinate System

Newton’s Second Law In Normal-Tangential Coordinate System

Newton’s Second Law In Polar Coordinate System

Work And Energy

Conservative Forces And Potential Energy

Principle Of Impulse And Momentum

Conservation Of Linear Momentum And Impacts

Angular Momentum

Planer Kinematics Of Rigid Bodies

Planer Dynamics Of Rigid Bodies

Work And Energy In Rigid Body Dynamics

Revision

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