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Physics 131 Equation Sheet: Fall 2007 - Prof. Andrew J. Dougherty, Quizzes of Mechanics

A collection of equations and formulas for various physics concepts covered in a university-level physics 131 course during the fall 2007 semester. Topics include kinematics, forces and potentials, work-energy, systems of particles, rotation, electric force and potential energy, vectors, and mathematics. This equation sheet can be used as a study aid for exam preparation.

Typology: Quizzes

Pre 2010

Uploaded on 08/19/2009

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Phys 131 Equation Sheet Fall 2007
Kinematics: v=v0+at x =x0+v0t+1
2at2v2=v2
0+ 2a(xx0)arad =v2
r
~vP/A =~vP/B +~vB /A
Forces and Potentials: ~
F=d~p
dt Ffr,s µsFNFf r,k =µkFNFs=k(xxR)
Us=1
2k(xxR)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 v2fv1f=(v2ivi1)
Rotation: θ=θ0+ω0t+1
2αt2ω=ω0+αt ω2=ω2
0+ 2α(θθ0)v=ωr
atan =αr arad =ω2r~
L=~r ×~p (particle) L= (rigid body) ~τ =~r ×~
F
I=X
i
mir2
iK=1
22X~τext =d~
L
dt Xτext = 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±b24ac
2a(1 + x)n1 + nx for x1
Constants: g= 9.8m/s2G= 6.67 ×1011Nm2/kg2REarth = 6.37 ×106m
MEarth = 5.98 ×1024 kg MSun = 1.99 ×1030kg c= 2.998 ×108m/s
e= 1.602 ×1019 Ck= 1/4π0= 8.988 ×109Nm2/C2
0= 8.854 ×1012 C2/Nm2me= 9.109 ×1031 kg

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Phys 131 Equation Sheet Fall 2007

Kinematics: v = v 0

  • at x = x 0

  • v 0

t +

at

2

v

2

= v

2

0

  • 2a(x − x 0

) a rad

v

2

r

~v P/A

= ~v P/B

  • ~v B/A

Forces and Potentials:

F =

d~p

dt

F

f r,s

≤ μ s

F

N

F

f r,k

= μ k

F

N

F

s

= −k(x − x R

U

s

k(x − x R

2 ~ F g

GM 1 M 2

r

2

rˆ U g

GM 1 M 2

r

T

2

=

4 π

2 r

3

GM

Work-Energy: W =

∫ r 2

r 1

F · d~r W =

F · ~r Ki + Wtot = Kf P =

F · ~v

∆UAB = −

∫ B

A

F · d~r Fx = −

dU

dx

Systems of Particles: ~p = m~v

F =

d~p

dt

M x cm

= m 1

x 1

  • m 2

x 2

i

m i

x i

F

ext

= M~a c

m v 2 f

− v 1 f

= −(v 2 i

− v i 1

Rotation: θ = θ 0

  • ω 0

t +

αt

2 ω = ω 0

  • αt ω

2 = ω

2

0

  • 2α(θ − θ 0

) v = ωr

a tan

= αr a rad

= ω

2 r

L = ~r × p~ (particle) L = Iω (rigid body) ~τ = ~r ×

F

I =

i

mir

2

i

K =

2

~τext =

d

L

dt

τext = Iα I = Icm + M d

2

K =

M V

2

cm

I

cm

ω

2

Electric Force and Potential Energy:

F = k

q 1

q 2

r

2

rˆ U = k

q 1

q 2

r

Vectors: Ax = A cos θ Ay = A sin θ A =

A

2

x

+ A

2

y

A ·

B = AB cos φAB

A ·

B = A

x

B

x

+ A

y

B

y

+ A

z

B

z

A ×

B = ˆnAB sin φ AB

Math: ax

2

  • bx + c = 0 x =

−b ±

b

2 − 4 ac

2 a

(1 + x)

n ≈ 1 + nx for x  1

Constants: g = 9.8m/s

2 G = 6. 67 × 10

− 11 Nm

2 /kg

2 R Earth

= 6. 37 × 10

6 m

MEarth = 5. 98 × 10

24

kg MSun = 1. 99 × 10

30

kg c = 2. 998 × 10

8

m/s

e = 1. 602 × 10

− 19 C k = 1/ 4 π 0

= 8. 988 × 10

9 Nm

2 /C

2

 0 = 8. 854 × 10

− 12

C

2

/Nm

2

me = 9. 109 × 10

− 31

kg