CRC Press - Mechanical Engineering Handbook- Mechanics Of Solids Part 5 ppsx

1-40 Section 1 (1.3.25a) Time Rate of Change of Angular Momentum In general, a force acting on a particle changes its angular momentum: the time rate of change of angular momentum of a particle is equal to the sum of the moments of the forces acting on the particle. A special case is when the sum of the moments about point O is zero. This is the conservation of angular momentum. In this case (motion under a central force), if the distance r increases, the velocity must decrease, and vice versa. Impulse and Momentum Impulse and momentum are important in considering the motion of particles in impact. The linear impulse and momentum equation is (1.3.28) Conservation of Total Momentum of Particles Conservation of total momentum occurs when the initial momentum of n particles is equal to the final momentum of those same n particles, (1.3.29) When considering the response of two deformable bodies to direct central impact, the coefficient of restitution is used. This coefficient e relates the initial velocities of the particles to the final velocities, (1.3.30) Hijk Ox y z xzy yxz zyx HHH H m yv zv H m zv xv H m xv yv =++ =− () =− () =− () Vectors: ˙ ( )HrvrFH OO d dt m=× () =× = ∑∑ 1326 Scalars: MH MH MH xx yy zz ∑∑∑ === ˙˙˙ MHrv OO m==×= () ∑ 0 1327 constant conservation of angular momentum ( . . ) t t dt m m 1 2 21 ∫ =− impulse final momentum initial momentum { { { Fvv mm ii i n t ii i n t vv () = () ∑∑ 12 12 total initial momentum at time total final momentum at time 1243412434 e vv vv Bf Af AB = − − = relative velocity of separation relative velocity of approach . 1-4 0 Section 1 (1.3.25a) Time Rate of Change of Angular Momentum In general, a force acting on a particle changes its angular momentum: the time rate of change of angular momentum of a particle. of particles in impact. The linear impulse and momentum equation is (1.3.28) Conservation of Total Momentum of Particles Conservation of total momentum occurs when the initial momentum of n particles. particle is equal to the sum of the moments of the forces acting on the particle. A special case is when the sum of the moments about point O is zero. This is the conservation of angular momentum. In