Solution Problem of the Week – 11
Here is a device consisting of four heavy metal balls connected together by rods whose
mass is negligible. Its center of mass is moving to the right with speed 10 m/s, and it is
rotating counterclockwise with angular speed 45 radians/s. (Use the usual convention for
the coordinate axes: x to the right, y towards the top of the page, and z out of the page
towards the reader.)
(a)
Calculate the translational angular momentum of the device relative to location
A
.
The translational angular momentum about point A is given by:
!
L
trans
,
A
=
!
R
CM
,
A
!
!
P
CM
where
!
R
CM
,
A
is a vector from point
A
to the location of the CM at the instant shown in the
figure.
Direction: The cross product on the right hand side gives the direction of the translational
angular momentum into the page, i.e., along the negative z direction.
Magnitude:
!
R
CM
,
A
=
.36,.30,0
m
!
P
CM
=
10
kg
!
10,0,0
m
/
s
=
100,0,0
kg
!
m
/
s
!
L
trans
,
A
=
0,0,
!
30
kg
"
m
2
/
s
,
!
L
trans
,
A
=
30
kg
!
m
2
/
s

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