Engineering Mechanics: Unit III: Distributed Forces

Perpendicular Axes Theorem (Area Moment of Inertia)

Statement, Proof, Diagram, Equation

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Statement: Moment of inertia of an area about an axis perpendicular to its plane

Perpendicular Axes Theorem

• Statement: Moment of inertia of an area about an axis perpendicular to its plane (i.e. the polar moment of inertia) at any point is equal to the sum of moments of inertia about any two mutually perpendicular axes through the same point in the plane of the area.

• Proof : Consider an area 'A' in X-Y plane as shown in Fig. 6.3.1.


The polar moment of inertia about the Z-axis passing through O is


Expressing these moments of inertia in terms of radii of gyration,


Engineering Mechanics: Unit III: Distributed Forces : Tag: : Statement, Proof, Diagram, Equation - Perpendicular Axes Theorem (Area Moment of Inertia)

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Engineering Mechanics: Unit III: Distributed Forces


Centroid - Introduction

Centre of Gravity, Centre of Mass and Centroid - with Solved Example Problems

Solved Example & Practice Problems: Centre of Gravity, Centre of Mass and Centroid

Centroid of Composite Areas - General procedure to find centroid of composite areas, Solved Example Problems

Solved Example & Practice Problems: Centroid of Composite Areas

Pappus-Guldinus Theorems - with Solved Example Problems

Solved Example & Practice Problems: Pappus-Guldinus Theorems - surface areas, volumes of bodies of revolution

Two Marks Questions with Answers - Centroid | Distributed Forces | Engineering Mechanics

Moment of Inertia of Plane Area

Radius of Gyration - Statement, Diagram, Equation | Moment of Inertia

Perpendicular Axes Theorem (Area Moment of Inertia) - Statement, Proof, Diagram, Equation

Parallel Axes Theorem (Area Moment of Inertia) - Statement, Proof, Diagram, Equation

Moment of Inertia by Integration (From First Principles)

Moment of Inertia of Composite Areas - with Solved Example Problems

Solved Example & Practice Problems: Moment of Inertia of Composite Areas

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