Find the inertia matrix for the following unit-density bodies in IR3 A solid cone z ≥ (x2 + y2)1/2 and 0 ≤ z ≤ 3 The union of thin discs {x2 + y2 ≤ R2 and z = 0} and {y2 + z2 ≤ R2 and x = 0}

Find the inertia matrix for the following unit-density bodies in IR3 A solid cone z ≥ (x2 + y2)1/2 and 0 ≤ z ≤ 3 The union of thin discs {x2 + y2 ≤ R2 and z = 0} and {y2 + z2 ≤ R2 and x = 0}

International Edition---engineering Mechanics: Statics, 4th Edition

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter9: Moments And Products Of Inertia Of Areas

Section: Chapter Questions

Problem 9.26P: A circular region of radius R/2 is cut out from the circular region of radius R as shown. For what...

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Concept explainers

Moment of Inertia

Inertia can be termed as a resistance offered by a body to change its state. A rigid body initially at rest will apply resistance when acted by an external force that tends to change its state of rest or velocity, or a body initially at motion will provide resistance in changing its state of velocity or motion for coming to a state of rest. In other words, Newton's first law of motion describes the law of inertia of a rigid body.

Question

Find the inertia matrix for the following unit-density bodies in IR³

A solid cone z ≥ (x² + y²)^1/2 and 0 ≤ z ≤ 3
The union of thin discs {x² + y² ≤ R² and z = 0} and {y² + z² ≤ R² and x = 0}

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