Find the center of mass and the moment of inertia about the y-axis for a thin plate bounded by the x-axis, the lines x = ±1, and the parabola y = x² if 8(x,y)=7y + 2. The coordinates of the plate's center of mass are x = and y = (Simplify your answers. Type integers or simplified fractions.)

Find the center of mass and the moment of inertia about the y-axis for a thin plate bounded by the x-axis, the lines x = ±1, and the parabola y = x² if 8(x,y)=7y + 2. The coordinates of the plate's center of mass are x = and y = (Simplify your answers. Type integers or simplified fractions.)

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 9.87RP

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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 center of mass and the moment of inertia about the y-axis for a thin
plate bounded by the x-axis, the lines x = ±1, and the parabola y=x² if
8(x,y) = 7y+2.
The coordinates of the plate's center of mass are x = and y =
(Simplify your answers. Type integers or simplified fractions.)

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Step 1: calculate moment about x axis

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