Subjects/Basic Physics/Linear momentum, impulse and collisionsSection 7Linear momentum, impulse and collisionsLinear momentumCopy LaTeXp=mvView detail →Second law in momentum formCopy LaTeX∑F=dtdpFor constant mass∑F=maView detail →ImpulseCopy LaTeXJ=∫titfFdtFor constant forceJ=FΔtView detail →Impulse-momentum theoremCopy LaTeXJ=Δp=pf−piView detail →Conservation of linear momentumCopy LaTeX∑pi=∑pfnegligible net external impulse.View detail →Perfectly inelastic 1D collisionCopy LaTeXm1v1i+m2v2i=(m1+m2)vfthe objects remain joined together after the collision.View detail →Elastic collisionCopy LaTeXMomentum is conservedm1v1i+m2v2i=m1v1f+m2v2fand the kinetic energy21m1v1i2+21m2v2i2=21m1v1f2+21m2v2f2View detail →Center of massCopy LaTeXrCM=∑imi∑imiriFor a continuous distributionrCM=M1∫rdmView detail →Center-of-mass velocityCopy LaTeXvCM=M∑imivi=MPtotalView detail →
Perfectly inelastic 1D collisionCopy LaTeXm1v1i+m2v2i=(m1+m2)vfthe objects remain joined together after the collision.View detail →
Elastic collisionCopy LaTeXMomentum is conservedm1v1i+m2v2i=m1v1f+m2v2fand the kinetic energy21m1v1i2+21m2v2i2=21m1v1f2+21m2v2f2View detail →