Fowles & Cassidy
are in direct impact with each other and have equal ani Defore impact, rebound with velocities that are, apart from the sign, the same." "The sum of the products of the magnitudes of each hard body, multiplied by the square of the velocities, is always the same, before and after the collision." — Christiaan Huygens, memoir, De Motu Corporum ex mutuo impulsu Hypothesis, composed in Paris, 5-Jan-1669, to Oldenburg, Secretary of the Royal Society 7.11 Introduction: Center of Mass and Linear Momentum of a System We now expand our study of mechanics of systems of many particles (two or more). These particles may or may not move independently of one another. Special systems, called rigid bodies, in which the relative positions of all the particles are fixed are taken up in the next two chapters. For the present, we develop some general theorems that apply to all sys- tems. Then we apply them to some simple systems of free particles. Our general system consists of n particles of masses m1, m2,. , whose position vectors are, respectively, r1, r2, . , We define the center of mass of the system as the point whose position vector (Figure 7.1.1) is given by = m1r1 + m2r2 +• + r = (7.1.1) m1 + m2 + m m = E the total mass of the system. The definition in Equation 7.1.1 is equiv- alent to the three equations — — — (7.1.2) m m m 275 276 CHAPTER 7 Dynamics of Systems of Particles z S S S S Center of mass y Figure 7.1.1 Center of mass of a system S of particles.
[Show full text]