340
Angular Momentum
Additional Problems
*P11.43
First, we define the following symbols:
I
P
=
moment of inertia due to mass of people on the equator
I
E
=
moment of inertia of the Earth alone (without people)
ω
=
angular velocity of the Earth (due to rotation on its axis)
T
==
2
π
rotational period of the Earth (length of the day)
R
=
radius of the Earth
The initial angular momentum of the system (before people start running) is
LI
I
I I
iP
iE
i
PE
i
=+=
+
ωω
bg
When the Earth has angular speed
, the tangential speed of a point on the equator is
vR
t
=
.
Thus, when the people run eastward along the equator at speed
v
relative to the surface of the Earth,
their tangential speed is
vv
v
R
v
pt
=+= +
and their angular speed is
P
p
v
R
v
R
+
.
The angular momentum of the system after the people begin to run is
I
I
v
R
II
I
Iv
R
fP
pE
P
E
P
=+
F
H
G
I
K
J
+=
+
+
ωωω
.
Since no external torques have acted on the system, angular momentum is conserved
LL
fi
=
di
,
giving
R
P
i
++
=
+
. Thus, the final angular velocity of the Earth is
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .
 Fall '11
 Staff
 Physics, Angular Momentum, Inertia, Mass, Momentum

Click to edit the document details