008 (part 1 of 2) 10.0 points
A
merry-go-round
rotates
at
the
rate
of
0
.
47 rev
/
s with an 98 kg man standing at
a point 2 m from the axis of rotation.
What is the new angular speed when the
man walks to a point 0 m from the center?
Consider the merry-go-round is a solid 57 kg
cylinder of radius of 2 m.
Correct answer: 13
.
1076 rad
/
s.
Explanation:
Given :
ω
i
= 0
.
47 rev
/
s
,
m
= 98 kg
,
r
i
= 2 m
,
r
f
= 0 m
,
M
= 57 kg
,
and
R
= 2 m
.
The merry-go-round can be modeled as a
solid disk with angular momentum
L
d
=
I
d
ω
=
parenleftbigg
1
2
M R
2
parenrightbigg
ω
and the man as a point mass with angular
momentum
L
m
=
I
m
ω
=
(
m r
2
)
ω .
Angular momentum is conserved, so
L
f
=
L
i
L
m,f
+
L
d,f
=
L
m,i
+
L
d,i
I
m,f
ω
f
+
I
d
ω
f
=
I
m,i
ω
i
+
I
d
ω
i
parenleftbigg
m r
2
f
+
1
2
M R
2
parenrightbigg
ω
f
=
parenleftbigg
m r
2
i
+
1
2
M R
2
parenrightbigg
ω
i
ω
f
=
1
2
M R
2
+
m r
2
i
1
2
M R
2
+
m r
2
f
ω
i
=
1
2
(57 kg) (2 m)
2
+ (98 kg) (2 m)
2
1
2
(57 kg) (2 m)
2
+ (98 kg) (0 m)
2
×
(0
.
47 rev
/
s)
·
2
π
rev
=
13
.
1076 rad
/
s
.
009 (part 2 of 2) 10.0 points
What is the change in kinetic energy due to
this movement?
Correct answer: 7586
.
77 J.
Explanation:
The moment of inertia of the system about
the axis of rotation at any moment is
I
=
I
d
+
I
m
=
1
2
M R
2
+
m r
2
,

kuruvila (lk5992) – HW 11 – opyrchal – (11113)
5
and the kinetic energy at any time is
K
rot
+
K
trans
=
1
2
I ω
2
=
1
2
parenleftbigg
1
2
M R
2
+
m r
2
parenrightbigg
ω
2
=
1
4
M R
2
ω
2
+
1
2
m r
2
ω
2
Thus the change in kinetic energy of the sys-
tem is
∆
K
=
K
f
−
K
i
=
parenleftbigg
1
4
M R
2
+
1
2
m r
2
f
parenrightbigg
ω
2
f
−
parenleftbigg
1
4
M R
2
+
1
2
m r
2
i
parenrightbigg
ω
2
i
=
bracketleftbigg
(57 kg)(2 m)
2
4
+
(98 kg)(0 m)
2
2
bracketrightbigg
×
(13
.
1076 rad
/
s)
2
−
bracketleftbigg
(57 kg)(2 m)
2
4
+
(98 kg)(2 m)
2
2
bracketrightbigg
×
(0
.
47 rev
/
s)
2
(2
π
rad
/
rev)
2
=
7586
.
77 J
.
010
10.0 points
A star of radius 7
.
8
×
10
5
km rotates about
its axis with a period of 44 days.
The star
undergoes a supernova explosion, whereby its
core collapses into a neutron star of radius
23 km.
Estimate the period of the neutron star
(assume the mass remains constant).

#### You've reached the end of your free preview.

Want to read all 5 pages?

- Spring '08
- moro
- Angular Momentum, Mass, Moment Of Inertia, Rotation