Ch17_Summary

# Ch17_Summary - bee29400_ch17_1080-1143.indd Page 1135...

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1135 REVIEW AND SUMMARY In this chapter we again considered the method of work and energy and the method of impulse and momentum. In the first part of the chapter we studied the method of work and energy and its applica- tion to the analysis of the motion of rigid bodies and systems of rigid bodies. In Sec. 17.2, we first expressed the principle of work and energy for a rigid body in the form T 1 1 U 1 y 2 5 T 2 (17.1) where T 1 and T 2 represent the initial and final values of the kinetic energy of the rigid body and U 1 y 2 represents the work of the external forces acting on the rigid body. In Sec. 17.3, we recalled the expression found in Chap. 13 for the work of a force F applied at a point A , namely U 1 y 2 5 # s 2 s 1 ( F cos a ) ds (17.3 9 ) where F was the magnitude of the force, a the angle it formed with the direction of motion of A , and s the variable of integration mea- suring the distance traveled by A along its path. We also derived the expression for the work of a couple of moment M applied to a rigid body during a rotation in u of the rigid body: U 1 y 2 5 # u 2 u 1 M d u (17.5) We then derived an expression for the kinetic energy of a rigid body in plane motion [Sec. 17.4]. We wrote T 5 1 2 mv 2 1 1 2 I v 2 (17.9) where v is the velocity of the mass center G of the body, v is the angular velocity of the body, and I is its moment of inertia about an axis through G perpendicular to the plane of reference (Fig. 17.13) [Sample Prob. 17.3]. We noted that the kinetic energy of a rigid body in plane motion can be separated into two parts: (1) the kinetic energy 1 2 mv 2 associated with the motion of the mass center G of the body, and (2) the kinetic energy 1 2 I v 2 associated with the rotation of the body about G. Principle of work and energy for a rigid body Work of a force or a couple Kinetic energy in plane motion G w Fig. 17.13

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1136 Plane Motion of Rigid Bodies: Energy and
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## This note was uploaded on 12/05/2011 for the course MEEG 324 taught by Professor Ib during the Fall '10 term at The Petroleum Institute.

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