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# Ch12 - bee76985_ch12_691-754 13:23 Page 691 CHAPTER 12...

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Caption to come 12 CHAPTER Kinetics of Particles: Newton’s Second Law

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692 12.1. INTRODUCTION Newton’s first and third laws of motion were used extensively in stat- ics to study bodies at rest and the forces acting upon them. These two laws are also used in dynamics; in fact, they are sufficient for the study of the motion of bodies which have no acceleration. However, when bodies are accelerated, that is, when the magnitude or the direction of their velocity changes, it is necessary to use Newton’s second law of motion to relate the motion of the body with the forces acting on it. In this chapter we will discuss Newton’s second law and apply it to the analysis of the motion of particles. As we state in Sec. 12.2, if the resultant of the forces acting on a particle is not zero, the parti- cle will have an acceleration proportional to the magnitude of the re- sultant and in the direction of this resultant force. Moreover, the ra- tio of the magnitudes of the resultant force and of the acceleration can be used to define the mass of the particle. In Sec. 12.3, the linear momentum of a particle is defined as the product L m v of the mass m and velocity v of the particle, and it is demonstrated that Newton’s second law can be expressed in an al- ternative form relating the rate of change of the linear momentum with the resultant of the forces acting on that particle. Section 12.4 stresses the need for consistent units in the solution of dynamics problems and provides a review of the International Sys- tem of Units (SI units) and the system of U.S. customary units. In Secs. 12.5 and 12.6 and in the Sample Problems which follow, Newton’s second law is applied to the solution of engineering prob- lems, using either rectangular components or tangential and normal components of the forces and accelerations involved. We recall that an actual body—including bodies as large as a car, rocket, or airplane—can be considered as a particle for the purpose of analyz- ing its motion as long as the effect of a rotation of the body about its mass center can be ignored. The second part of the chapter is devoted to the solution of prob- lems in terms of radial and transverse components, with particular emphasis on the motion of a particle under a central force. In Sec. 12.7, the angular momentum H O of a particle about a point O is de- fined as the moment about O of the linear momentum of the parti- cle: H O r m v . It then follows from Newton’s second law that the rate of change of the angular momentum H O of a particle is equal to the sum of the moments about O of the forces acting on that particle. Section 12.9 deals with the motion of a particle under a central force, that is, under a force directed toward or away from a fixed point O. Since such a force has zero moment about O , it follows that the angular momentum of the particle about O is conserved. This property greatly simplifies the analysis of the motion of a particle under a central force; in Sec. 12.10 it is applied to the solution of
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