University Physics Volume 1

# Key Equations

### Key Equations

 Definition of momentum $p→=mv→p→=mv→$ Impulse $J→≡∫titfF→(t)dtorJ→=F→aveΔtJ→≡∫titfF→(t)dtorJ→=F→aveΔt$ Impulse-momentum theorem $J→=Δp→J→=Δp→$ Average force from momentum $F→=Δp→ΔtF→=Δp→Δt$ Instantaneous force from momentum(Newton’s second law) $F→(t)=dp→dtF→(t)=dp→dt$ Conservation of momentum $dp→1dt+dp→2dt=0orp→1+p→2=constantdp→1dt+dp→2dt=0orp→1+p→2=constant$ Generalized conservation of momentum $∑j=1Np→j=constant∑j=1Np→j=constant$ 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 $F→ext=∑j=1Ndp→jdtF→ext=∑j=1Ndp→jdt$ Newton’s second law for an extended object $F→=dp→CMdtF→=dp→CMdt$ Acceleration of the center of mass $a→CM=d2dt2(1M∑j=1Nmjr→j)=1M∑j=1Nmja→ja→CM=d2dt2(1M∑j=1Nmjr→j)=1M∑j=1Nmja→j$ Position of the center of mass for a system of particles $r→CM≡1M∑j=1Nmjr→jr→CM≡1M∑j=1Nmjr→j$ Velocity of the center of mass $v→CM=ddt(1M∑j=1Nmjr→j)=1M∑j=1Nmjv→jv→CM=ddt(1M∑j=1Nmjr→j)=1M∑j=1Nmjv→j$ Position of the center of mass of acontinuous object $r→CM≡1M∫r→dmr→CM≡1M∫r→dm$ Rocket equation $Δv=uln(mim)Δv=uln(mim)$