Problem
9
-
10.5.40
:
Three
children
are
riding
on
the
edge
of
a
merry-go-round
that
is
a
disk
of
mass
92
kg,
radius
7.7
m,
and
is
spinning
at
15
rpm.
The
children
have
masses
of
20.4
kg,
26
kg.
and
31
kg.
=
Randomized
Variables
M=92kg
my=204kg
my;=26kg
my=231kg
r=11m
f=151pm
Part
(o)
If
the
child
who
has
a
mass
of
¢
kg
moves
to
the
center
of
the
merry-go-round,
what
is
the
new
magnitude
of
angular
velocity
in
rpm?
To solve
this
problem,
we
can
use
the
conservation
of
angular
momentum.
However,
in
order
to
do
so,
we
will
first
need
to
find
the
imitial
angular
velocity,
the
initial
moment
of inertia,
and
the
final
moment
of
inertia.
We
already
kmow
the
initial
angular
velocity
in
rpm,
so
let's
begin
by
finding
the
initial
moment
of
inertia.
We
can
do
this
by
summing
up
the
moment
of
nertia
of
the
merry-go-round
itself
(which
we
will
approximate
as
a
disk)
together
with
the
moments
of
inertia
of the
children.
I
—;-Mrz
Fmgr?
mar®
4+
myrt
We
can
find
an
expression
for
the
final
moment
of
inertia
using
the
same
strategy.
This
time,
however,
the
second
child
will
be
at
the
exact
center
of
the
merry-go-round,
meaning
that
they
are
at
an
effective
radius
of
0.
I
%[v{rz
Pyt
mz(O)2
+
mgr?
I
%Mrz
b
mart
Now;,
let's
write
an
equation
for
the
conservation
of
angular
momentum
and
solve
for
the
final
angular
velocity.
L-L
I!
II,I
If
,
7
f
f(-;Mf'z
Fmur?
+
mar®
+
mar?)
f’
%M,J
{
mn"
t
m;"z
5
f(-;—Mlmnlszm;)
%M
tmy
|+
my
#
15rpm
-
(3
-92kg
+204ke
|
26kg
|
31kg)
L1.92kg
|
204kg
|
31kg
