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ghei (mg42382) – HW 8 – opyrchal – (11130)
1
This printout should have 14 questions.
Multiplechoice questions may continue on
the next column or page – fnd all choices
beFore answering.
001
10.0 points
The angular position oF an object that rotates
about a fxed axis is given by
θ
(
t
) =
θ
0
e
βt
,
where
β
= 3 s

1
,
θ
0
= 0
.
7 rad, and
t
is in
seconds.
What is the magnitude oF the total linear
acceleration at
t
= 0 oF a point on the object
that is 8
.
4 cm From the axis?
Correct answer: 64
.
5971 cm
/
s
2
.
Explanation:
Let :
r
= 8
.
4 cm
.
We can fnd the angular velocity and accel
eration:
θ
(
t
) =
θ
0
e
βt
ω
(
t
) =
d θ
(
t
)
dt
=
β θ
0
e
βt
and
α
(
t
) =
d ω
(
t
)
dt
=
β
2
θ
0
e
βt
.
At
t
= 0, since
e
0
= 1,
ω
=
β θ
0
and
α
=
β
2
θ
0
,
so the tangential and radial accelerations are
a
t
=
αr
=
β
2
θ
0
r
and
a
r
=
ω
2
r
=
β
2
θ
2
0
r ,
and the magnitude oF the total linear acceler
ation is
a
=
r
a
2
t
+
a
2
r
=
r
β
4
θ
2
0
r
2
+
β
4
θ
4
0
r
2
=
β
2
θ
0
r
r
1 +
θ
2
0
= (3 s

1
)
2
(0
.
7 rad) (8
.
4 cm)
r
1 + (0
.
7 rad)
2
=
64
.
5971 cm
/
s
2
.
002 (part 1 of 2) 10.0 points
A ±ywheel with a very low Friction bearing
takes 1
.
4 h to stop aFter the motor power
is turned o².
The ±ywheel was originally
rotating at 47 rpm.
What was the initial rotation rate in radi
ans per second?
Correct answer: 4
.
92183 rad
/
s.
Explanation:
Let :
f
= 47 rpm
.
ω
0
= (47 rpm)
2
π
rev
1 min
60 sec
=
4
.
92183 rad
/
s
.
003 (part 2 of 2) 10.0 points
How many revolutions does the ±ywheel make
beFore it stops?
Correct answer: 1974 rev.
Explanation:
Let :
t
= 1
.
4 h
.
The angular acceleration oF the ±ywheel is
α
=

ω
0
t
,
so the angle is
θ
=
ω
0
t
+
1
2
α t
2
=
ω
0
t
+
1
2
p

ω
0
t
P
t
2
=
1
2
ω
0
t
=
1
2
(4
.
92183 rad
/
s) (1
.
4 h)
3600 s
1 h
1 rev
2
π
=
1974 rev
.
004 (part 1 of 2) 10.0 points
A small turtle, appropriately named “Dizzy”,
is placed on a horizontal, rotating turntable at
a distance oF 21
.
6 cm From its center. Dizzy’s
mass is 54
.
8 g, and the coe³cient oF static
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View Full Documentghei (mg42382) – HW 8 – opyrchal – (11130)
2
friction between his feet and the turntable is
0
.
32.
Find the maximum angular velocity the
turntable can have if Dizzy is to remain sta
tionary relative to the turntable. The accel
eration of gravity is 9
.
8 m
/
s
2
.
Correct answer: 0
.
606431 rev
/
s.
Explanation:
Let :
r
= 21
.
6 cm = 0
.
216 m
,
m
= 54
.
8 g
,
μ
= 0
.
32
,
and
g
= 9
.
8 m
/
s
2
.
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 Spring '09
 WANG
 Physics

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