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001
(part 1 oF 2) 10.0 points
A skater spins with an angular speed oF
17
.
4 rad
/
s with his arms outstretched.
He
lowers his arms, decreasing his moment oF in
ertia From 43 kg
·
m
2
to 37 kg
·
m
2
.
a) Calculate his initial rotational kinetic
energy.
Correct answer: 6509
.
34 J.
Explanation:
Basic Concepts:
L
=
Iω
KE
=
1
2
Iω
2
Given:
I
i
= 43 kg
·
m
2
I
f
= 37 kg
·
m
2
ω
i
= 17
.
4 rad
/
s
Solution:
KE
i
=
1
2
I
i
ω
2
i
=
1
2
(43 kg
·
m
2
)(17
.
4 rad
/
s)
2
= 6509
.
34 J
002
(part 2 oF 2) 10.0 points
b) Calculate his fnal rotational kinetic en
ergy.
Correct answer: 7564
.
91 J.
Explanation:
Solution:
Angular momentum oF the system is con
served, so
I
f
ω
f
=
I
i
ω
i
ω
f
=
I
i
ω
i
I
f
KE
f
=
1
2
I
f
p
I
i
ω
i
I
f
P
2
=
1
2
I
2
i
ω
2
i
I
f
=
1
2
(43 kg
·
m
2
)
2
(17
.
4 rad
/
s)
2
37 kg
·
m
2
= 7564
.
91 J
003
(part 1 oF 3) 10.0 points
Assume:
The small objects are point parti
cles.
The system oF fve small 2 kg objects is
rotating at an angular speed oF 3 rad
/
s. The
objects are connected by light, ±exible spokes
that can be lengthened or shortened.
x
y
2 kg
2 kg
2 kg
2 kg
2 kg
3
r
a
d
/
s
m
What is the initial angular momentum oF
the object?
Note:
An e²ect similar to this ocurred
in the early stages oF the Formation oF our
Galaxy. As the massive cloud oF dust and gas
that was the source oF the stars and planets
contracted, an initially small angular speed
increased with time.
Correct answer: 270 kg m
2
/
s.
Explanation:
Basic Concepts:
The angular momentum
is
L
=
I ω
=
(
M r
2
)
ω .
With no external
torques, angular momentum is concerved.
Let :
m
= 2 kg
,
r
1
= 3 m
,
r
2
= 7 m
,
and
ω
1
= 3 rad
/
s
.
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 Spring '08
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