Chapter 9 Center of Mass and Linear Momentum In this chapter we will introduce the following new concepts: -Center of mass (com) for a system of particles -The velocity and acceleration of the center of mass -Linear momentum for a single particle and a system of particles We will derive the equation of motion for the center of mass, and discuss the principle of conservation of linear momentum. Finally, we will use the conservation of linear momentum to study collisions in one and two dimensions and derive the equation of motion for rockets. (9-1)

(9-2)

(9-3)

(9-4). C C

O m1m1 m3m3 m2m2 F1F1 F2F2 F2F2 x y z (9-5)

O m1m1 m3m3 m2m2 F1F1 F2F2 F2F2 x y z (9-6)

(9-7)

m v p (9-8)

O m1m1 m3m3 m2m2 p1p1 p2p2 p3p3 x y z (9-9)

(9-10)

(9-11)

(9-12) F ave

O m1m1 m3m3 m2m2 p1p1 p2p2 p3p3 x y z (9-13)

(9-14)

(9-15)

(9-16)

m m m m v1iv1i v 1f = 0v2fv2f v 2i = 0 x x (9-17)

(9-18) v 2i = 0 m1m1 m1m1 m2m2 m2m2 v1iv1i v1fv1f v2fv2f x x

m1m1 m1m1 m2m2 m2m2 v1iv1i v1fv1f v2fv2f x x (9-19)

(9-20)

(9-21)

vfvf vivi Mi/MfMi/Mf O (9-22)