89.1 Momentum and Newton 's second law of motion 1. momentum (1)a single particle of mass m Define:p=mν=m (2 a group of particles of mass m1,m2,…,m,… ∑i P1=∑mv Position vector of center of mass 2. the center of mass Total The total momentum of a system of particle: P- p=∑n=∑ dr d M dt 89.1 Momentum and Newtons second law of motion (1)The position vector of mass center(weighted average) Define: =∑ M 元1+22+ M That is IcM= m1F1+m2F2+…+mN m1+m2+…+mN Total mass of the particle system M=n n1+n,+…+n1 122 1. momentum (1)a single particle of mass m Define: t r p mv m d d r r r = = (2)a group of particles of mass m1, m2, …, mi , … = ∑ = ∑ i i i i i p p m v r r r 2. the center of mass ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =∑ =∑ = ∑ i i i i i i i i M m r t M t r p p m r r r r d d d d The total momentum of a system of particle： t r p M d d CM r r = ? Position vector of center of mass Total mass §9.1 Momentum and Newton’s second law of motion x y z 1r r Nr r m1 m2 mN O 2 r r (1)The position vector of mass center (weighted average) N N N m m m m r m r m r r + + + + + + = L r L r r r 1 2 1 1 2 2 CM That is N N i i i r M m r M m r M m M m r r r L r r r r = + + + = ∑ 2 2 1 1 CM Define: M = mtotal = m1 + m2 +L+ mN Total mass of the particle system: C c r r §9.1 Momentum and Newton’s second law of motion