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Some Equations for Exam 2
•
For this exam, use the approximation that
g
=10m
/
s
2
.
•
For a function
f
(
x
)=
ax
n
, where
n
is an integer,
df
dx
=
nax
n

1
.
•
Work by
±
F
moving from
i
to
f
:
W
=
±
f
i
±
F
·
d±s
Power:
P
=
dW
dt
•
Kinetic energy:
K
=
1
2
mv
2
; for rotating bodies,
K
=
1
2
Iω
2
.
•
Potential energy: Δ
U
=

±
f
i
±
F
·
for a conservative force; and
F
x
=

∂U
∂x
, etc.
•
Gravitational potential energy near the Earth’s surface:
U
=
mgh
.
•
For an ideal spring, force:
F
=

kx
; potential energy:
U
=
1
2
2
.
•
For a system,
W
ext
=Δ
E
mec
K
+Δ
U
. For an isolated system,
W
ext
= 0, so
E
mec
is constant and Δ
K
U
=0
.
•
Momentum:
±p
=
m±v
;
Newton’s 2
nd
Law:
±
F
=
d±p
dt
.
•
For a system with Σ
±
F
ext
,
tot
= const
.
•
Position of the center of mass:
±r
cm
=
1
M
Σ
m
i
i
,
where
M
=Σ
m
i
.
•
Angular velocity:
ω
=
dφ
dt
. Angular acceleration:
α
=
dω
dt
.
•
For a constant angular acceleration,
ω
=
ω
0
+
αt
and
φ
=
φ
0
+
ω
0
t
+
1
2
αt
2
.
•
For circular motion, the tangential component of acceleration is
a
t
=
αr
; the radial
(centripetal) component is
a
r
=
v
2
/r
=
ω
2
r
.
•
Rotational inertia, or moment of inertia:
I
=
±
r
2
dm
.
–
for a solid sphere about any diameter:
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This note was uploaded on 04/30/2008 for the course PHY 317k taught by Professor Kopp during the Fall '07 term at University of Texas at Austin.
 Fall '07
 KOPP
 Energy, Kinetic Energy, Power, Work

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