The initial angular velocity of the system is
i
= 0.20 rev/s = 1.26 rad/s, and we find the
final angular velocity via conservation of angular momentum, as
f
=
I
i
I
f
i
=
370
130
(1.26 rad/s)
= 3.6 rad/s.
(b)
The change in kinetic energy is
KE
f

KE
i
=
1
2
I
f
f
2

1
2
I
i
i
2
, or
=
1
2
(130 kg m
2
)(3.58 rad/s)
2

1
2
(370 kg m
2
)(1.26 rad/s)
2
= 540 J.
This difference results from work done by the man on the system as he walks inward.
•
A cylinder with moment of inertia
I
1
rotates about a vertical,
frictionless axle with angular velocity v
i
.
A second cylinder, this
one having moment of inertia
I
2
and initially not rotating, drops
onto the first cylinder. Because of friction between the surfaces,
the two eventually reach the same angular velocity
v
f
.
•
(a) Calculate v
f
.
•
(b) Show that the kinetic energy of the system decreases in this
interaction and calculate the ratio of the final to the initial
rotational energy.
(a)
From conservation of angular momentum for the system of two cylinders:
1
2
1
f
i
I I
I
or
1
1
2
f
i
I
I I
(b)
2
1
2
1
2
f
f
K
I I
and
2
1
1
2
i
i
K
I
so
2
1
1
2
2
1
1
2
1
1
2
1
2
1
2
which is less than 1
f
i
i
i
K
I I
I
I
K
I I
I I
I
.
•
A puck of mass
m
is
attached to a cord passing
through a small hole in a
frictionless, horizontal
surface. The puck is
initially orbiting with
speed
v
i
in a circle of
radius
r
i
. The cord is then
slowly pulled from below,
decreasing the radius of
the circle to
r
.
•
(a) What is the speed of
the puck when the radius
is
r
?
•
(b) Find the tension in the
cord as a function of
r
.
(a)
sin180 0
r F rF
Angular momentum is conserved.
f
i
i i
i i
L
L
mrv mrv
rv
v
r
(b)
2
2
3
i i
m rv
mv
T
r
r
FIG. P11.49
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 Fall '12
 Vesna
 Physics, Angular Momentum, Moment Of Inertia, Rotation, kg, cricket