physics 140 final cheatsheet

# physics 140 final cheatsheet - Gen Info...

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Moment Inertia :K=1/2Iω 2 ,I p =I CM +Md 2 ,I=∫r 2 dm=∫r 2 ρdV Disk,Rod&Masses :w(h)=√(2m 1 gh/(I tot +m 1 r 2 )),I tot =I d +I r +2M 2 R 2 Hooke’sLaw :stress/strain=elastic modulus (proportionality constant) = bulk mod. B =bulk strain/bulk stress=Δp/(detaV/V 0 ) compressibility k=1/B Young’s Mod .:Y=tensile stress/tensile strain=(F/A)/(ΔL/L 0 )=F/A Shear Mod :S=shear stress/shear strain=(F/A)/(x/h) h=init.height,x=disp. of 1side Fluid Pressure : p=F/A=ρgh Breaking stress =ultimate strength-where material breaks Proportional limit =max stress where Hooke’s law is still valid. Gen. Info: 1mi=1609m,100cm=1m,1000g=1kg,1in=5.4cm,N=kg·m/s 2 ,J=kg·m 2 /s 2 =N·m Cos rule: A 2 +B 2 -ABcosC,sin rule: sin(b)/B=sin(a)/A,density ρ=m·V, weight w = m·g, tension T=((m 1 +m 2 )/ m 1 m 2 )g(1+sin(θ)) Atwoods: [if m 1 >m 2 ] Rocket Eqn : m(t)=m 0 -Rt,V(t)=V 0 +V exh ·ln|m 0 /m(t)| a 1 =a 2 =a T 1 =T 2 =T m(t)=R·V exh /a=Ru/a m 0 Δv=Δm exh u m 1 : m 1 g-T=m 1 a mΔvΔt=Δm/Δt·u m 2 : T-m 2 g=m 2 a m(t)a=Ru a=(m 1 g-m 2 g)/m 1 m 2 Scalar : #s, normal arithmetic, dot product C=A·B=ABcosθ Vector : dir. & magnitude, C=AxB=ABsinθ, x+y=r, r=√(x 2 +y 2 ) Uniform v&a/ω&α : avg.v=Δx/Δt,v=x’,avg.a=Δv/Δt,a=v’ v=v 0 +at, x=x 0 +v 0 t+1/2at 2 , v 2 =v 0 2 +2a(x-x 0 ), x-x 0 =(v 0 +v)/2·t, v=v 0 +∫adt,x=x 0 +∫vdt ω=dθ/dt,α=dω/dt, θ=θ 0 0 t+1/2αt 2 , Δθ=1/2Δωt, ω=ω 0 +αt, ω 2 0 2 +2αΔθ Proj.Motion : a x =0,a y =g,x=v 0 cosθ·t,y=v 0 sinθ·t-1/2gt 2 ,v x =v 0 cosθ,v y =v 0 sinθ-gt R=v 0 2 sin(2θ)/g, H=v 0 2 sin 2 θ/2g, t peak =v 0y /g, H/R=tanθ/4 Freefall/Horiz.: t=√(2h/g),v y =√(2gh),v 0 =R√(g/2h),=1/2gt 2 Circ.Motion :a r :a ┴ v,affects direction,a r =v 2 /R=4π 2 R/T 2 ,T=2πR/v,a t =a//v,affects speed,a t =v’,v=rω, a t =rα,a r 2 r Rel.Veloc .:v P/A =v P/B +v B/A Newton’s Laws : 1.Σ[email protected] 2.ΣF=ma 3.F A/B = -F B/A Friction/Drag k k

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