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Key Equations

Definition of momentum p=mvp=mv
Impulse JtitfF(t)dtorJ=FaveΔtJtitfF(t)dtorJ=FaveΔt
Impulse-momentum theorem J=ΔpJ=Δp
Average force from momentum F=ΔpΔtF=ΔpΔt
Instantaneous force from momentum
(Newton’s second law)
F(t)=dpdtF(t)=dpdt
Conservation of momentum dp1dt+dp2dt=0orp1+p2=constantdp1dt+dp2dt=0orp1+p2=constant
Generalized conservation of momentum j=1Npj=constantj=1Npj=constant
Conservation of momentum in two dimensions pf,x=p1,i,x+p2,i,xpf,y=p1,i,y+p2,i,ypf,x=p1,i,x+p2,i,xpf,y=p1,i,y+p2,i,y
External forces Fext=j=1NdpjdtFext=j=1Ndpjdt
Newton’s second law for an extended object F=dpCMdtF=dpCMdt
Acceleration of the center of mass aCM=d2dt2(1Mj=1Nmjrj)=1Mj=1NmjajaCM=d2dt2(1Mj=1Nmjrj)=1Mj=1Nmjaj
Position of the center of mass for a system
of particles
rCM1Mj=1NmjrjrCM1Mj=1Nmjrj
Velocity of the center of mass vCM=ddt(1Mj=1Nmjrj)=1Mj=1NmjvjvCM=ddt(1Mj=1Nmjrj)=1Mj=1Nmjvj
Position of the center of mass of a
continuous object
rCM1MrdmrCM1Mrdm
Rocket equation Δv=uln(mim)Δv=uln(mim)
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