Problem 4. For the solid shape that is defined from 0 to 1 on x and y as two straight edges and the curve givenbelow, with y equal to the square root of x, find the centroid and moment of inertia at the centroid about x and yaxes, as well as about the base and left side using Parallel-Axis Theorem.y10y=xl/21X

To find the centroid and moment of inertia of the solid shape described, we first need to determine…

Answered: y 0 y=xl/2

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Mechanical Engineering

y 0 y=xl/2

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

4th Edition

ISBN:9781305501607

Author:Andrew Pytel And Jaan Kiusalaas

Publisher:Andrew Pytel And Jaan Kiusalaas

Chapter8: Centroids And Distributed Loads

Section: Chapter Questions

Problem 8.70P: Use numerical integration to find the centroid of the volume generated by revolving the area shown...

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Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and after loading.

Question

Problem 4. For the solid shape that is defined from 0 to 1 on x and y as two straight edges and the curve given
below, with y equal to the square root of x, find the centroid and moment of inertia at the centroid about x and y
axes, as well as about the base and left side using Parallel-Axis Theorem.
y
1
0
y=xl/2
1
X

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Step 1: Find the Area and Centroid of the Shape

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Step 2: Moment of Inertia at the Centroid (about x and y axes)

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Step 3: Final Results The centroid of the shape is at (1/2, 2/3).

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