THEORYMECHANICSChapter11MomentumtheoremCollege of Mechanical and Vehicle EngineeringWangXiaojun
College of Mechanical and Vehicle Engineering WangXiaojun THEORY MECHANICS Chapter11 Momentum theorem
Chapter11 Momentumtheorem11.1momentum11. 2momentum theorem11.3The center of mass motion theorem
• 11. 1 momentum • 11. 2 momentum theorem • 11. 3 The center of mass motion theorem Chapter11 Momentum theorem
$11.1momentum1 momentum: P=mvsize: mv ;1.1 Momentum of particle:The direction is determined by :unit: kg?m /sP=Zm,Vi1.2 Momentumoftheparticle systemM=≥The total mass of the particle system ismm,r2Mr.=-Zmrm
1 momentum 1.1 Momentum of particle： P = mv size: ； The direction is determined by ； unit: kgm /s v mv The total mass of the particle system is: M = mi c = i i M r m r 1.2 Momentum of the particle system: = i i P m v = i i i c m m r r §11.1 momentum
$11.1 momentumMv.=ZmyAfterderivationtoP= MveThatis,the productof the mass of a system of particles and the velocityofits centerofmassequalsthemomentumofthesystem ofparticlesP= mv= mxCalculation method:XcxCprojection methodP= mv= myJcyp：= mv= mzCz
P = Mvc That is, the product of the mass of a system of particles and the velocity of its center of mass equals the momentum of the system of particles. After derivation to = i i M vc m v Calculation method: projection method X cx c P = mv = mx y cy c P = mv = my z cz c P = mv = mz §11.1 momentum
$11.1 momentumExamplel: As shown in the figure, it is known that the mass of crank OC isM, the mass of gauge AB is 2m, and the mass of slider A and B are mboth,OC=CA=CB= l. Find the momentum of the ellipse gauge as the crankrotates at angular velocity at the indicated position.VAAPSolution:Take thewholerigidbody system as the researchVcobject.Themomentumofthewhole system isVB0B
Example1：As shown in the figure, it is known that the mass of crank OC is M, the mass of gauge AB is 2m, and the mass of slider A and B are both,OC=CA=CB= . Find the momentum of the ellipse gauge as the crank rotates at angular velocity at the indicated position. m l C A B O P v A v B vC Solution: Take the whole rigid body system as the research object.The momentum of the whole system is §11.1 momentum