{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Caption to come 12 CHAPTER Kinetics of Particles: Newton’s Second Law
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern