学 质点 动量定理:质点系动量的改变→外力(外力系主矢) 质心运动定理:质心的运动—→>外力(外力系主矢) 若当质心为固定轴上一点时,v=0,则其动量恒等于零, 质心无运动,可是质点系确受外力的作用。动量矩定理建立了 质点和质点系相对于某固定点(固定轴)的动量矩的改变与外 力对同一点(轴)之矩两者之间的关系
6 质点 动量定理： 质点系 动量的改变—→外力（外力系主矢） 若当质心为固定轴上一点时，vC=0，则其动量恒等于零， 质心无运动，可是质点系确受外力的作用。动量矩定理建立了 质点和质点系相对于某固定点（固定轴）的动量矩的改变与外 力对同一点（轴）之矩两者之间的关系。 质心运动定理：质心的运动—→外力（外力系主矢）
Dynamic 813-1 Moment of momentum Moment of momentum of a particle with respect to a center O is (mv)=r× mi it is a vector Moment of momentum of a particle with respect to an axis Zis m (mv)=mo(mv,)it is an algebraic qu mo(mv)=240AB B m(m)=±2△OB mmv The definition o of the sis he sign of the moment of momentum with respect to an axis is the same as that of the y moment of a force with respect to an axis. Looking from the positive end of the axis, it's positive if it is counterclockwise, and it is negative if it is clockwise 7
7 §13-1 Moment of momentum Moment of momentum of a particle with respect to a center O is , it is a vector. Moment of momentum of a particle with respect to an axis Z is , it is an algebraic quantity. m mv r mv O ( )= ( ) ( ) z O xy m mv =m mv mO (mv) =2OAB m (mv) 2 OA'B' z = The definition of the sign of the moment of momentum with respect to an axis is the same as that of the moment of a force with respect to an axis. Looking from the positive end of the axis, it’s positive if it is counterclockwise, and it is negative if it is clockwise
学 §13-1动量矩 质点的动量矩 质点对点O的动量矩:m(mV)=F×m失量 质点对轴z的动量矩:m2(m)=m0(mn)代数量 B z、mv m(m)=2A04B m2(m)=±2△O4B mo(mv) 正负号规定与力对轴矩的规定相同 对着轴看:顺时针为负 ArMy 逆时针为正
8 §13-1 动量矩 一．质点的动量矩 质点对点O的动量矩： 矢量 质点对轴 z 的动量矩： 代数量 m mv r mv O ( )= ( ) ( ) z O xy m mv =m mv mO (mv) =2OAB m (mv) 2 OA'B' z = 正负号规定与力对轴矩的规定相同 对着轴看：顺时针为负 逆时针为正
Dynarnics The relation between the moment of momentum of a particle with respect to an axis and a center is mo(mv):=m(mv Moment of momentum measures the intensity of rotation of a body rotating around a fixed center or an axis at any instant. kg. m/s 2. Moment of momentum of a system of particles. The moment of momentum of a system with respect to a center O is 1o=∑m(m2v1)=∑×mn1v The moment of momentum of a system with respect to an axis Zis L=∑m:(m)=ol Calculation of moment of momentum of a rigid body. 1)Rigid body in translational motion Lo=mo(mv=rc xmv (ΣXm=m×=xm)L=m(m) The moment of momentum of a rigid body in translational motion with respect to a fixed center(axis) is equal to the moment of momentum of the center of mass of the rigid body with respect to that center(axis)
9 The relation between the moment of momentum of a particle with respect to an axis and a center is 2. Moment of momentum of a system of particles. The moment of momentum of a system with respect to a center O is The moment of momentum of a system with respect to an axis Z is O O i i i mi vi L =m (m v )=r z z i i LO z L =m (m v )= kg·ｍ2 /s. Moment of momentum measures the intensity of rotation of a body rotating around a fixed center or an axis at any instant. m (mv) m (mv) O z = z Calculation of moment of momentum of a rigid body. 1) Rigid body in translational motion O O C C C L =m (mv )=r mv ( ) i i i i i C C mvC r m v =m r v =r ( ) z z C L =m mv The moment of momentum of a rigid body in translational motion with respect to a fixed center (axis) is equal to the moment of momentum of the center of mass of the rigid body with respect to that center (axis)
力单 质点对点O的动量矩与对轴z的动量矩之间的关系 Imo(mv))=m(mv 动量矩度量物体在任一瞬时绕固定点(轴)转动的强弱kgm2/s 质点系的动量矩 质系对点O动量矩:L=∑m0(m1,)=∑xm1 质系对轴z动量矩:L:=∑m(m)=[一 刚体动量矩计算: 1.平动刚体 o=mo(mvc)=×mc (∑Xm21=∑mF×WC=1xmC) =m (mvo) 平动刚体对固定点(轴)的动量矩等于刚体质心的动量 对该点(轴)的动量矩。 10
10 质点对点O的动量矩与对轴z 的动量矩之间的关系： 二．质点系的动量矩 质系对点O动量矩： 质系对轴z 动量矩： O O i i i i i L =m (m v )=r m v z z i i LO z L =m (m v )= kg·ｍ2 动量矩度量物体在任一瞬时绕固定点(轴)转动的强弱 /s。 m (mv) m (mv) O z = z 刚体动量矩计算： 1．平动刚体 O O C C C L =m (mv )=r mv ( ) i i i i i C C C r m v =m r v =r mv ( ) z z C L =m mv 平动刚体对固定点（轴）的动量矩等于刚体质心的动量 对该点（轴）的动量矩