sanchez (ds28677) – homework 25 – Turner – (58220)
1
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001
(part 1 of 2) 10.0 points
A skater
spins
with an
angular
speed
of
17
.
9 rad
/
s with his arms outstretched.
He
lowers his arms, decreasing his moment of in
ertia from 43 kg
·
m
2
to 36 kg
·
m
2
.
a) Calculate his initial rotational kinetic
energy.
Correct answer: 6888
.
81 J.
Explanation:
Basic Concepts:
L
=
Iω
KE
=
1
2
Iω
2
Given:
I
i
= 43 kg
·
m
2
I
f
= 36 kg
·
m
2
ω
i
= 17
.
9 rad
/
s
Solution:
KE
i
=
1
2
I
i
ω
2
i
=
1
2
(43 kg
·
m
2
)(17
.
9 rad
/
s)
2
= 6888
.
81 J
002
(part 2 of 2) 10.0 points
b) Calculate his final rotational kinetic en
ergy.
Correct answer: 8228
.
31 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
parenleftbigg
I
i
ω
i
I
f
parenrightbigg
2
=
1
2
I
2
i
ω
2
i
I
f
=
1
2
(43 kg
·
m
2
)
2
(17
.
9 rad
/
s)
2
36 kg
·
m
2
= 8228
.
31 J
003
(part 1 of 3) 10.0 points
Assume:
The small objects are point parti
cles.
The system of nine small 6 kg objects is
rotating at an angular speed of 7 rad
/
s. The
objects are connected by light, flexible spokes
that can be lengthened or shortened.
x
y
6 kg
6 kg
6 kg
6 kg
6 kg
6 kg
6 kg
6 kg
6 kg
7
r
a
d
/
s
8 m
What is the initial angular momentum of
the object?
Note:
An effect 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: 24192 kg m
2
/
s.
Explanation:
BasicConcepts:
The angular momentum
is
L
=
I ω
=
(
M r
2
)
ω .
With no external
torques, angular momentum is concerved.
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sanchez (ds28677) – homework 25 – Turner – (58220)
2
Let :
m
= 6 kg
,
r
1
= 8 m
,
r
2
= 9 m
,
and
ω
1
= 7 rad
/
s
.
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 Spring '08
 Turner
 Physics, Angular Momentum, Work, Correct Answer, kg, Sanchez

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