Version PREVIEW – OH10 – Bradley – (191)
1
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17
questions.
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before answering.
This is Online Homework No.
10.
It is
due 06:00 AM Tuesday morning 4 November
(Abu Dhabi Time), unless notified otherwise.
Turntable Comes to a Stop
001
(part 1 of 2) 5.0 points
The turntable of a record player rotates at a
rate of 45
.
7 rev
/
min and takes 64
.
2 s to come
to rest when switched off.
Find the deceleration.
Correct answer: 0
.
0745435 rad
/
s
2
.
Explanation:
Let :
ω
0
= 45
.
7 rev
/
min
,
t
= 64
.
2 s
,
and
ω
f
= 0
.
The angular acceleration is
α
=
Δ
ω
Δ
t
=
ω
f

ω
0
Δ
t
=

ω
0
Δ
t
=

45
.
7 rev
/
min
64
.
2 s
2
π
1 rev
1 min
60 s
=

0
.
0745435 rad
/
s
2
,
a deceleration of
0
.
0745435 rad
/
s
2
.
002
(part 2 of 2) 5.0 points
How many revolutions did it make before
coming to rest?
Correct answer: 24
.
4495 rev.
Explanation:
For a deceleration of
α
, the angle is
θ
=
ω
0
t

1
2
α t
2
= (45
.
7 rev
/
min)(64
.
2 s)
1 min
60 sec

1
2
(0
.
0745435 rad
/
s
2
) (64
.
2 s)
2
1 rev
2
π
=
24
.
4495 rev
.
Rigid Rectangular System 02
003
(part 1 of 2) 5.0 points
Four particles with masses 5 kg, 6 kg, 5 kg,
and 2 kg are connected by rigid rods of neg
ligible mass as shown.
Aassume the system
rotates in the
xy
plane about the
z
axis (ori
gin,
O
) with an angular speed of 4 rad
/
s.
x
y
O
4 rad
/
s
9 m
8 m
5 kg
6 kg
5 kg
2 kg
Find the moment of inertia of the system
about the
z
axis.
Correct answer: 652
.
5 kg
·
m
2
.
Explanation:
Let :
m
1
= 5 kg
,
top left
m
2
= 6 kg
,
bottom left
m
3
= 5 kg
,
bottom right
m
4
= 2 kg
,
top right
w
= 8 m
,
and
h
= 9 m
.
Each mass is a distance
d
=
radicalBigg
parenleftBig
w
2
parenrightBig
2
+
parenleftbigg
h
2
parenrightbigg
2
=
radicalbigg
w
2
+
h
2
4
from the axis of rotation, so
I
z
=
summationdisplay
i
m
i
r
2
i
=
d
2
summationdisplay
i
m
i
=
w
2
+
h
2
4
summationdisplay
i
m
i
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Version PREVIEW – OH10 – Bradley – (191)
2
=
(8 m)
2
+ (9 m)
2
4
(18 kg)
=
652
.
5 kg
·
m
2
.
004
(part 2 of 2) 5.0 points
Find the rotational energy of the system
about the
z
axis.
Correct answer: 5220 J.
Explanation:
Let :
ω
= 4 rad
/
s
.
The rotational energy of the system is
K
=
1
2
I
z
ω
2
=
1
2
(652
.
5 kg
·
m
2
) (4 rad
/
s)
2
=
5220 J
.
Swinging Rod 02
005
10.0 points
A massless rod of length
L
has a mass 2
m
fastened at its center and another mass
m
fastened at one end.
On the opposite end
from the mass
m
, the rod is hinged with a
frictionless hinge.
The rod is released from
rest from an initial horizontal position; then
it swings down.
What is the maximum angular velocity as
the rod swings through its lowest (vertical)
position?
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 Spring '08
 curtise
 Angular Momentum, Kinetic Energy, Moment Of Inertia, Correct Answer, kg, ABU DHABI

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