Center of Mass and Linear Momentum 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)

. C (9-4)

O m1 m3 m2 F1 F2 x y z (9-5)

O m1 m3 m2 F1 F2 x y z (9-6)

(9-7)

m v p (9-8)

O m1 m3 m2 p1 p2 p3 x y z (9-9)

(9-10)

(9-11)

Fave (9-12)

O m1 m3 m2 p1 p2 p3 x y z (9-13)

(9-14)

(9-15)

(9-16)

m v1i v1f = 0 v2f v2i = 0 x (9-17)

v2i = 0 m1 m2 v1i v1f v2f x (9-18)

m1 m2 v1i v1f v2f v2i = 0 x (9-19)

(9-20)

(9-21)

vf vi Mi/Mf O (9-22)