University of Minnesota
School of Physics
and Astronomy
Physics
130L, Section
200, Fall 2008
Name:
Student
ID No:
TA Name:
Hour Exam 4: Problem 1
[Friday,
November 2L,2008)
fPlease
do the problem on the front and back of this sheet of paper.]
The Earth travels around the Sun
in a nearly circular orbit with a radius of L.50 x 1011
m.
The period of the Earth's orbit is one year or 365.24 solar days. The Earth also rotates on
its axis
in one solar day. The Earth can be simply modeled
as a solid, homogenous
sphere
with a radius of 6378 km and a mass of the Earth
is 5.97 x 1024
kg.
[aJ
What is the orbital angular momentum of the Earth as
it travels around the Sun.
[10
points)
[b)
What is the angular momentum of the Earth as
it rotates on its axis?
(10 points)
[c)
The Earth's orbital angular momentum and rotational angular momentum can be
represented by vectors. The two vectors point generally
in the same direction,
that is, both
the orbital motion and the rotational motion are counterclockwise,
when viewed from the
direction of the Earth's or Sun's North Pole. The angle between
the two vectors
is23.44".
What is the Earth's
total angular momentum.
C
r,r=
p1
JT.
crt
I
t
l

o( \2
:
rll
36S.
L(lx
2q K
L6oo
\4
r^,rQ
\,Lu,rl L=
LV'J
=
\"!$I
xu.u1*t.qq\xb'
Sun
=.
t.qllxt^ct
r*J&
ftStu.tne eorlL
i"'>
"
rot',f
WV*u
J cr
QDn
.\.
,
o
L
f.,\q",^
/
r,t
=
5,11
x1oz't"SYc
)
b)
61

$5\
I

a,.t
Lo"ts,",,=
?6r5
xt"t{o
b*'/s*
Q,g,uv.
.
I
=
T
(r
r
\ LJ
t*,
*,
=
\"1
glt
Ts,
/tb
x1
rys
$4
K
,"11xti)

Grrv*{
,\
n?
,
\,1l+Xr,o'''
k^
^nt
)
a+
x 36oo
I
I
x,J'
T

l"
3+!x
r,o(l
\^'
6
.,
ug.oh"W
c^
= 111
x
t=
,oJ/q
vu3
.
\
.
\
'' ')
'
retp
h^5
g"s\iu\
s"$\.".e
to
!=
s
'c'J.21
X u'c'
L5
*
=
'J.0
6x