In a homogeneous gravitational field the centers of mass and the center gravity coincide. Using any method of determination of the center of gravity determines the position of the center of mass of a system. But they are not identical. The concept of the center of mass has more mechanical meaning than that of the center of gravity. 2. External forces and internal forces of a system of particles External forces are the forces exerted on the members of a system by particles or bodies not belonging to the given system Internal forces are the forces of interaction between the members of the same system As far as the whole system of particles is concerned, the geometrical sum(the principal vector) of all the internal forces of a system is zero The sum of the moments(the principal moment of all the internal forces of a system with respect to any center of axis is zero, too ∑F=0,∑而()=00∑m(F)=0。m
11 In a homogeneous gravitational field the centers of mass and the center gravity coincide.Using any method of determination of the center of gravity determines the position of the center of mass of a system. But they are not identical. The concept of the center of mass has more mechanical meaning than that of the center of gravity. External forces are the forces exerted on the members of a system by particles or bodies not belonging to the given system Internal forces are the forces of interaction between the members of the same system. As far as the whole system of particles is concerned, the geometrical sum (the principal vector) of all the internal forces of a system is zero. The sum of the moments (the principal moment )of all the internal forces of a system with respect to any center of axis is zero, too. Fi (i) = 0; mO (Fi (i) ) = 0 or mx (Fi (i) ) = 0。 2. External forces and internal forces of a system of particles:
学 在均匀重力场中,质点系的质心与重心的位置重合。可采 用静力学中确定重心的各种方法来确定质心的位置。但是,质 心与重心是两个不同的概念,质心比重心具有更加广泛的力学 意义。 二、质点系的内力与外力 外力:所考察的质点系以外的物体作用于该质点系中各质点的力。 内力:所考察的质点系内各质点之间相互作用的力 对整个质点系来讲,内力系的主矢恒等于零,内力系对任 点(或轴)的主矩恒等于零。即: ∑F=0.∑m0(F)=0或∑m、(F①)=0。 12
12 在均匀重力场中，质点系的质心与重心的位置重合。可采 用静力学中确定重心的各种方法来确定质心的位置。但是，质 心与重心是两个不同的概念，质心比重心具有更加广泛的力学 意义。 内力：所考察的质点系内各质点之间相互作用的力。 对整个质点系来讲，内力系的主矢恒等于零，内力系对任一 点（或轴）的主矩恒等于零。即： Fi (i) =0; mO (Fi (i) )=0 或 mx (Fi (i) )=0。 二、质点系的内力与外力 外力：所考察的质点系以外的物体作用于该质点系中各质点的力
Dynamics 8 12-2 Momentum and impulse 1. Momentum 1) Momentum of a particle. The product of the mass of a particle and its velocity is called the momentum of a particle. It is a time-dependent vector with the same direction as the velocity, the unit of which is kg m/s Momentum is a physical quantity measuring the intensity of the mechanical motion of a material body For example, the velocity of a bullet is big but its mass is small. In the case of a boat it is Just opposite. 13
13 §12-2 Momentum and impulse 1. Momentum 1) Momentum of a particle.The product of the mass of a particle and its velocity is called the momentum of a particle. It is a time-dependent vector with the same direction as the velocity, the unit of which is kgm/s. Momentum is a physical quantity measuring the intensity of the mechanical motion of a material body. For example, the velocity of a bullet is big but its mass is small. In the case of a boat it is just opposite
学 §12-2动量与冲量 动量 1.质点的动量:质点的质量与速度的乘积mv称为 质点的动量。是瞬时矢量,方向与ν相同。单位是 kg. m/s 动量是度量物体机械运动强弱程度的一个物理量。 例:枪弹:速度大,质量小;船:速度小,质量大 14
14 §12-2 动量与冲量 一、动量 1.质点的动量：质点的质量与速度的乘积 mv 称为 质点的动量。 是瞬时矢量，方向与v 相同。单位是 kgm/s。 动量是度量物体机械运动强弱程度的一个物理量。 例：枪弹：速度大，质量小； 船：速度小，质量大
2) The momentum of a system of particles is defined as the vector equal to the geometric sum of the momenta of all the particles of the system K=∑m=MCc ifferent iate the equation >m=Mrc with respect to time. The momentum of a system is equal to the product of the mass of the whole system and the velocity of its center of mass. In terms of projections on cartesian axes we have K,=MG=Mc, K,=MG=Mic, K=MVc=MEc 3)Momentum of a system of rigid bodies: Assume that the mss and the velocity of the center of mass of the i-th rigid body arem, v For the whole system we get then K,F∑ma=∑m, K=∑m,K=∑mvcn=∑myc K:=∑mc=2m=a.15
15 2) The momentum of a system of particles is defined as the vector equal to the geometric sum of the momenta of all the particles of the system: i i C K =m v =Mv (Different iate the equation with respect to time.) i i C m r = Mr x Cx C y Cy C z Cz C K =Mv =Mx , K =Mv =My , K =Mv =Mz 3)Momentum of a system of rigid bodies: Assume that the mss and the velocity of the center of mass of the i-th rigid body are . For the whole system we get then i ci m ,v = 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 The momentum of a system is equal to the product of the mass of the whole system and the velocity of its center of mass. In terms of projections on cartesian axes we have . . . , , .