634_Dynamics 11ed Manual

634_Dynamics 11ed Manual - = k G 2 r GO = Q.E.D Problem...

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Engineering Mechanics - Dynamics Chapter 19 Problem 19-1 The rigid body (slab) has a mass m and is rotating with an angular velocity ω about an axis passing through the fixed point O. Show that the momenta of all the particles composing the body can be represented by a single vector having a magnitude mv G and acting through point P , called the center of percussion , which lies at a distance r PG = k 2 G / r GO from the mass center G. Here k G is the radius of gyration of the body, computed about an axis perpendicular to the plane of motion and passing through G. Solution: H o r GO r PG + () mv G = r GO mv G I G + = Where I G mk G 2 = r GO mv G r PG mv G + r GO mv G mk G 2 + = r PG k G 2 v G = k G 2 v G v G r GO
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Unformatted text preview: = k G 2 r GO = Q.E.D Problem 19-2 At a given instant, the body has a linear momentum L = mv G and an angular momentum H G = I G computed about its mass center. Show that the angular momentum of the body computed about the instantaneous center of zero velocity IC can be expressed as H IC = I IC where I IC represents the bodys moment of inertia computed about the instantaneous axis of zero velocity. As shown, the IC is located at a distance r GIC away from the mass center G . Solution: H IC r GIC mv G I G + = Where v G r GIC = 632...
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This note was uploaded on 08/16/2011 for the course EGN 3321 taught by Professor Christianfeldt during the Spring '08 term at University of Central Florida.

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