89.1 Momentum and Newtons second law of motion (2)Momentum of system of particles ∑D=∑m dr M M M Ptotal M CM My CM (3)Kinetic energy of system of particles 十 =Vo+ 89.1 Momentum and Newton's second law of motion The total Kinetic energy of the whole system KEHI 722m2= ∑,m(x+的) (om +v 2 mv ∑ 2 v/+2vcM vi ∑m"+∑m+m:∑m可 KE=-MI 2 2 CM 2 v5 (2) Momentum of system of particles CM CM total d d Mv t r p M r r r = = t r M M m r t M t r p p m i i i i i i i i d d d d d d CM r r r r r =⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =∑ =∑ = ∑ (3) Kinetic energy of system of particles i i i i v v v r r r = + ′ = + ′ r r r r r r CM CM §9.1 Momentum and Newton’s second law of motion x y z mi O C rCM r i r r i r ′ r The total Kinetic energy of the whole system i i i i i i i i i i i i i i i i i i i i i i i m v m v v m v m v v v v m v v v v KE m v m v v = + ′ + ⋅ ′ = + ′ + ⋅ ′ = + ′ ⋅ + ′ = = ⋅ ∑ ∑ ∑ ∑ ∑ ∑ ∑ r r r r r r r r r r CM 2 2 CM CM 2 2 CM CM CM 2 total 2 1 2 1 ( 2 ) 2 1 ( ) ( ) 2 1 2 1 2 1 ∑ ′ = 0 i i i m v r 2 2 total CM 2 1 2 1 i i i KE = Mv +∑ m v′ §9.1 Momentum and Newton’s second law of motion