Download Understanding Momentum in Physics: Definition, Newton's Laws, and Conservation and more Slides Physics in PDF only on Docsity! Momentum docsity.com Physics Definition of Momentum • Momentum is another word (like work, energy, etc.) from everyday life that has a precise meaning when used in physics. • To begin with, we discuss point particles (or small enough bodies they can be considered points). We’ll get to bigger things soon. • The momentum of a particle of mass m moving with velocity is writtenv p mv= docsity.com Lots More Particles…. • Suppose we have a large number of particles, interacting with each other with forces , and also acted on by external forces, like gravity or electric fields. • One of the particles will have rate of change of momentum • If we add together the equations for all the particles, the internal forces cancel in pairs, leaving • The total momentum is only changed by external forces. ext intn n mn m n dp F F dt ≠ = +∑ extn n n n dP dp F dt dt = =∑ ∑ int mnF docsity.com Impulsive Force • A large force operating for a very short time is often termed an impulse. • If the force operates for a time , the impulse • Impulsive forces usually vary rapidly with time (as when a bat hits a ball), and then • An impulsive force causes a change in momentum equal to the impulse: F t∆ J F t= ∆ ( )J F t dt= ∫ final initial dpp p dt Fdt J dt − = = =∫ ∫ docsity.com Clicker Question Two balls of putty of equal mass approach each other from opposite directions at equal speeds. They stick together and come to rest. Was momentum conserved in this collision? A. Yes B. No docsity.com Center of Mass of Two Particles • If the two particles are at the ends of a light rod, their center of mass xCM is the point about which they would balance: and from this • A xCM - xA xB - xCM mA mB xA xCM xB x0( ) ( )A CM A B B CMm x x m x x− = − A A B B CM A B m x m xx m m + = + If the rod isn’t parallel to the x-axis, we need the three- dimensional version: A A B B CM A B m r m rr m m + = + docsity.com Center of Mass and Total Momentum • For two particles, writing the total mass the center of mass is given by and differentiating to find its time dependence Bottom line: the total momentum of the system equals the total mass multiplied by the CM velocity. A BM m m= + CM A A B BMr m r m r= + CM A A B B A BMv m v m v p p P= + = + = docsity.com Motion of the Center of Mass • We saw earlier that the total momentum of a system is only changed by external forces: • We now see that . • It follows that the motion of the center of mass is as if all the mass were concentrated there, and all the external forces acted there. • For zero external forces, is constant. extn n n n dP dp F dt dt = =∑ ∑ CMP Mv= CMv docsity.com
