2.质点系的动量:质点系中所有各质点的动量的矢量和。 K=∑m=MC(∑mF=M求导) 质点系的质量与其质心速度的乘积就等于质点系的动量。则: K,=MG=MC, K,=MC=MyC, K=Mc=ME 3刚体系统的动量:设第个刚体m1,a则整个系统: K2=∑ma=∑mx K=∑mva K,=∑m1Vc=2mya K:=∑mva=∑m:= 16
16 2.质点系的动量：质点系中所有各质点的动量的矢量和。 i i C K =m v =Mv ( 求导) i i C m r =Mr 质点系的质量与其质心速度的乘积就等于质点系的动量。则： x Cx C y Cy C z Cz C K =Mv =Mx , K =Mv =My , K =Mv =Mz 3.刚体系统的动量：设第i个刚体 mi ,vci 则整个系统： = i Ci K m v = = = = = = z i Ciz i Ci y i Ciy i Ci x i Cix i Ci K m v m z K m v m y K m v m x
EXample 1 In the mechanism shown in the figure, OA rotate with a constant angular velocity a Assume that Oa=L, OB=L The rods oa and ab are homogeneous and of mass m. The mass of the slide block at b is also m Determine the momentum of the system when (p=45. For the side block mass=m,vc3 21o. p Solution For the rod OA mass=m v=lo 77 For the rod AB: mass=m, VC2=N5-10AB 2 lo( point P is the instantaneous 2 center of velocity PC=L0=0 K=mv, +mv+my=v2mlot-2i+j1 -mlCvcisin-vc2c0sB-vc3)i +(vci cos@+vc2 sine)jI =mcolosin45' 50o2o)+(1oo45+5om 2 =mlo(-2× 3 7 222 221
17 PC = l, AB = 2 5 2 m v v v i K mv mv mv C C C C C C [( sin cos ) 1 2 3 1 2 3 = − − − = + + ( cos sin ) ] 1 2 v v j + C + C ) ] 10 1 2 5 2 2 2 1 2) ( 10 3 2 5 2 2 2 1 [( sin ) ] 2 5 cos45 2 1 cos 2 ) ( 2 5 sin45 2 1 [( m l i j m l l l i l l j = − − − + + = − − − + + ] 2 1 = 2ml[−2i + j m vC l 2 1 , 1 = m vC l AB l 2 5 2 5 , 2 = = m, vC3 = 2l ( point P is the instantaneous center of velocity ). [Example 1] In the mechanism shown in the figure, OA rotate with a constant angular velocity . Assume that OA=L,OB=L. The rods OA and AB are homogeneous and of mass m. The mass of the slide block at B is also m. Determine the momentum of the system when =45º. Solution. For the rod OA mass = . For the slide block mass = . For the rod AB: mass=
之学 〔例1〕曲柄连杆机构的曲柄OA以匀 O转动,设OA=AB=l,曲柄OA及连杆 AB都是匀质杆,质量各为m,滑块B的质 量也为m。求当q=45时系统的动量。 解:曲柄OA:m,V=2 滑块B:m,va3=√2lo 77 √5o510(P为速度瞬 连杆AB:mve2=2l0=2 心,PC2= 204B=0) K=mvci+mvc2+mvc3=v2mlo[-2i+5] =m[C-va sino-vc2 cos8-vc3)i +(vci cosp+vc2sin0)jl =m[(-losn45° /5 =mlo[a 52552 22 30 2+(×2+5×万 18
18 解: 曲柄OA： 滑块B： 连杆AB： （ P为速度瞬心， PC = l; AB = ） 2 5 2 〔例１〕曲柄连杆机构的曲柄OA以匀 转动，设OA=AB=l ,曲柄OA及连杆 AB都是匀质杆, 质量各为m , 滑块B的质 量也为m。求当 = 45º时系统的动量。 m v v v i K mv mv mv C C C C C C [( sin cos ) 1 2 3 1 2 3 = − − − = + + ( cos sin ) ] 1 2 v v j + C + C ) ] 10 1 2 5 2 2 2 1 2) ( 10 3 2 5 2 2 2 1 [( sin ) ] 2 5 cos45 2 1 cos 2 ) ( 2 5 sin45 2 1 [( m l i j m l l l i l l j = − − − + + = − − − + + ] 2 1 = 2ml[−2i + j m vC l 2 1 , 1 = m vC l AB l 2 5 2 5 , 2 = = m, vC3 = 2l