Final_EXAM_EQ_Sheet - 
 USEFUL
INFORMATION
 Δr = v...

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Unformatted text preview: 
 USEFUL
INFORMATION
 Δr = v avg Δt 

 Δp = Fnet Δt Mm Fgrav = G 2 ;
approx.
mg
near
surface
of
Earth
 r Fspring = ks s G = 6.7 × 10 −11 N·m2/kg2
 g
=
9.8
N/kg
 1 = 9 x10 9 Nm 2 / C 2 4 πε0 
 kB = 1.38 × 10 −23 J / K 
 p = mγv 
 γ= ,
opposite
the
stretch
 1 1− U electric = 1 q1q2 
 4 πε0 r 
 U gravity = 12 ks 
 2 
 
 12 mv 
for
a
single
particle
if
 v << c 
 2 1 Fair = Cρ air Av 2 2 
 Fbuoyancy = v c2 
 E = mγc 2 
for
a
single
particle
 E = mc 2 + p ≈ mv ,
if
 v 
is
small
compared
to
c
 
 
 ρ air mg ρ object 

 ΔE thermal = mCv ΔT 
 
 
 
 
 
 
 −GMm 
 r ! Fnet U spring = ΔE system = W surroundings + Q 2 c = 3 × 10 8 m/s
 mv 2 = m" 2 R 
 R ! = 
 f = µN 
 ! = 2" f = 2" 
 T 1 K trans = mv 2 2 W = F • Δr 
 ΔLA = τ A Δt I disk = I cylinder about l ong axis = 
 
 
 
 I sphere = 1 MR 2 2 2 MR 2 5 Moment
of
inertia
if
a
thin
cylinder
rotating
about
an
axis
perpendicular
to
the
 1 ML2 
 cylinder,
through
the
center
of
the
cylinder I cylinder = 12 
 
 τ A = rA × F I = ∑ mi ri 2 K total = K trans + K rot + K vib 
 
 dLtot , A τ net , A = 

 dt L2 1 K rot = rot = Iω 2 2I 2 LA = [ rCM × PTotal ] + [∑ ri , CM × pi ] = Ltrans + Lrot 
 i mass
of
earth
=
5.97
x
1024
kg
 
 
 radius
of
earth
=
6.4
x
106
m
 mass
of
sun
=
1.99
x
1030
kg

 
 
 mass
of
proton
=
1.67
x
10‐27
 
 
 
 1
eV
=
1.6
x
10‐19
J
 Room
temperature
=
300
K
 
 
 
 1
mol
=
6.02
x
1023
 mass
of
electron
=
9.11
x
10‐31
kg
 − ΔE Boltzmann
factor
=
 e kT 
 Ω= 
 (q + N − 1)! 
 q!( N − 1)! 
 ...
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This note was uploaded on 08/02/2011 for the course PHYS 172 taught by Professor ? during the Spring '08 term at Purdue University-West Lafayette.

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