Alvarado, Patrick – Homework 2 – Due: Sep 21 2006, 10:00 am – Inst: Andrei Sirenko
1
This
printout
should
have
22
questions.
Multiplechoice questions may continue on
the next column or page – find all choices
before answering.
The due time is Central
time.
001
(part 1 of 1) 10 points
Nobody at the playground wants to play with
an obnoxious boy, so he fashions a seesaw as
shown so he can play by himself.
Explain how this is done.
1.
The angular velocity of the boy is can
celled with that of the board.
2.
The weight of the boy is balanced with an
unknown heavy metal.
3.
The weight of the boy is balanced by the
weight of the board.
correct
4.
The fulcrum is very far from the boy.
Explanation:
The weight of the boy is counterbalanced by
the weight of the board, which can be consid
ered to be concentrated at its center of gravity
on the opposite side of the fulcrum. He is in
balance when his weight multiplied by his dis
tance from the fulcrum is equal to the weight
of the entire board multiplied by the distance
between the fulcrum and the midpoint (center
of gravity) of the board. (How do the relative
weight of boy and board relate to the relative
lever arms?)
keywords:
002
(part 1 of 1) 10 points
The net work done in accelerating a propeller
from rest to an angular speed of 306 rad
/
s is
1864 J.
What is the moment of inertia of the pro
peller?
Correct answer: 0
.
0398137 kg
·
m
2
.
Explanation:
Given :
W
= 1864 J
and
ω
= 306 rad
/
s
.
Using
W
= Δ
K
=
K
f

K
i
=
1
2
I ω
2

0
,
we get
I
=
2
W
ω
2
=
2 (1864 J)
(306 rad
/
s)
2
,
=
0
.
0398137 kg
·
m
2
.
keywords:
003
(part 1 of 1) 10 points
Consider the diatomic molecule oxygen, O
2
,
which is rotating in the
xy
plane about the
z
axis passing through its center, perpendicular
to its length. The mass of each oxygen atom
is 2
.
66
×
10

26
kg, and at room temperature,
the average separation distance between the
two oxygen atoms is 2
.
68
×
10

10
m(the atoms
are treated as point masses).
If the angular speed of the molecule about
the
z
axis is 3
.
55
×
10
12
rad
/
s, what is its
rotational kinetic energy?
Correct answer: 6
.
01933
×
10

21
J.
Explanation:
Since the distance of each atom form the
z
axis is
d/
2 (where
d
= 2
.
68
×
10

10
m is the
separation distance between the two oxygen
atoms), the moment of inertial about the
z
axis is
I
=
2
X
n
=1
m
n
r
2
n
=
m
d
2
¶
2
+
m
d
2
¶
2
=
1
2
m d
2
,
where
m
= 2
.
66
×
10

26
kg
is the mass of
an oxygen atom.
Using the formula for the
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Alvarado, Patrick – Homework 2 – Due: Sep 21 2006, 10:00 am – Inst: Andrei Sirenko
2
rotational kinetic energy, we obtain
K
R
=
1
2
I ω
2
=
1
4
m d
2
ω
2
= 6
.
01933
×
10

21
J
.
keywords:
004
(part 1 of 2) 10 points
Calculate the moment of inertia of a solid
cylinder of mass 5
.
68 kg and radius 8
.
14 m
about an axis parallel to the centerofmass
axis and passing through the edge of the cylin
der. (Use the parallelaxis theorem and Table
10.2)
Correct answer: 564
.
532 kg m
2
.
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 Spring '08
 OPYT
 Angular Momentum, Kinetic Energy, Work, Moment Of Inertia, Rigid Body, kg, Andrei Sirenko

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