Determine the moment of inertia of the area bounded by the curve y = 9 – x² and y =3x – x? at the first quadrant with respect to the x -axis. Also, determine the radius ofgyration.To solve this problem, it is important to graph the curves to visualize which curve lieabove or below the area bounded. Two methods can solve this problem both involvingintegration. First is by summing the moment of inertia of all differential centroidalmoment of inertia and applying the parallel axis theorem and second is by treating thebounded region as a composite area and subtracting the moment of inertia of two areasabove the x axis.Answers: (a) 328.05 units“ (b) 4.9295 units

The curves are:- 1) y=9-x2 2) y=3x-x2 To determine:- a) Moment of inertia of the shaded area b)…

Answered: Determine the moment of inertia of the…

Determine the moment of inertia of the area bounded by the curve y = 9- x² and y = 3x – x? at the first quadrant with respect to the x -axis. Also, determine the radius of gyration.

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

Determine the moment of inertia of the area bounded by the curve y = 9 – x² and y =
3x – x? at the first quadrant with respect to the x -axis. Also, determine the radius of
gyration.
To solve this problem, it is important to graph the curves to visualize which curve lie
above or below the area bounded. Two methods can solve this problem both involving
integration. First is by summing the moment of inertia of all differential centroidal
moment of inertia and applying the parallel axis theorem and second is by treating the
bounded region as a composite area and subtracting the moment of inertia of two areas
above the x axis.
Answers: (a) 328.05 units“ (b) 4.9295 units

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