Phys 131 Equation Sheet Fall 2007
Kinematics: v=v0+at x =x0+v0t+1
2at2v2=v2
0+ 2a(x−x0)arad =v2
r
~vP/A =~vP/B +~vB /A
Forces and Potentials: ~
F=d~p
dt Ffr,s ≤µsFNFf r,k =µkFNFs=−k(x−xR)
Us=1
2k(x−xR)2~
Fg=−GM1M2
r2ˆr Ug=−GM1M2
rT2=4π2r3
GM
Work-Energy: W=Zr2
r1
~
F·d~r W =~
F·~r Ki+Wtot =KfP=~
F·~v
∆UAB =−ZB
A
~
F·d~r Fx=−dU
dx
Systems of Particles: ~p =m~v ~
F=d~p
dt Mxcm =m1x1+m2x2+··· =X
i
mixi
X~
Fext =M~acm v2f−v1f=−(v2i−vi1)
Rotation: θ=θ0+ω0t+1
2αt2ω=ω0+αt ω2=ω2
0+ 2α(θ−θ0)v=ωr
atan =αr arad =ω2r~
L=~r ×~p (particle) L=Iω (rigid body) ~τ =~r ×~
F
I=X
i
mir2
iK=1
2Iω2X~τext =d~
L
dt Xτext =Iα I =Icm +M d2
K=1
2MV 2
cm +1
2Icmω2
Electric Force and Potential Energy: ~
F=kq1q2
r2ˆr U =kq1q2
r
Vectors: Ax=Acos θ Ay=Asin θ A =qA2
x+A2
y~
A·~
B=AB cos φAB
~
A·~
B=AxBx+AyBy+AzBz~
A×~
B= ˆnAB sinφAB
Math: ax2+bx +c= 0 x=−b±√b2−4ac
2a(1 + x)n≈1 + nx for x1
Constants: g= 9.8m/s2G= 6.67 ×10−11Nm2/kg2REarth = 6.37 ×106m
MEarth = 5.98 ×1024 kg MSun = 1.99 ×1030kg c= 2.998 ×108m/s
e= 1.602 ×10−19 Ck= 1/4π0= 8.988 ×109Nm2/C2
0= 8.854 ×10−12 C2/Nm2me= 9.109 ×10−31 kg