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Husain, Zeena – Homework 8 – Due: Oct 21 2003, 4:00 am – Inst: H L Berk
1
This printout should have 23 questions, check
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fnd all choices beFore making your selection.
The due time is Central time.
001
(part 1 oF 2) 10 points
A wheel starts From rest and rotates with
constant angular acceleration to an angular
speed oF 8
.
39 rad
/
s in 1
.
95 s.
±ind the magnitude oF the angular acceler
ation oF the wheel.
Correct answer: 4
.
30256 rad
/
s
2
.
Explanation:
Angular acceleration is defned by,
α
=
dω
dt
When the angular acceleration is constant,
we can replace the di²erentials with simply
di²erences,
α
=
Δ
ω
Δ
t
=
ω
f

ω
i
t
The angle through which the wheel rotates
during this time interval is,
θ
=
1
2
αt
2
002
(part 2 oF 2) 10 points
±ind the angle in radians through which it
rotates in this time.
Correct answer: 8
.
18025 rad.
Explanation:
003
(part 1 oF 1) 10 points
Given:
g
= 9
.
8 m
/
s
2
.
A car traveling on a ³at (unbanked, 9 m
radius) circular track accelerates uniFormly
From rest with a tangential acceleration oF
1
.
9 m
/
s
2
. The car makes it 0
.
4 oF the way
around the circle beFore skidding o² the track.
Determine the coe´cient oF static Friction
between car and track.
Correct answer: 0
.
993633 .
Explanation:
Given :
θ
= 0
.
4 rev = 2
.
51327 rad
,
r
= 9 m
,
a
t
= 1
.
9 m
/
s
2
,
and
g
= 9
.
8 m
/
s
2
.
Just beFore it starts to skid the Force equations
are
X
F
r
=
m a
r
=
m v
2
r
=
m ω
2
r ,
X
F
t
=
m a
t
,
or
μ m g
=
q
(
m a
t
)
2
+ (
m ω
2
r
)
2
.
ThereFore,
μ
=
s
µ
a
t
g
¶
2
+
µ
ω
2
r
g
¶
2
=
s
µ
a
t
g
¶
2
+
µ
2
α θ r
g
¶
2
=
s
µ
a
t
g
¶
2
+
µ
2
a
t
θ
g
¶
2
=
µ
a
t
g
¶
q
1 + [2
θ
]
2
=
µ
1
.
9 m
/
s
2
9
.
8 m
/
s
2
¶
q
1 + [2(2
.
51327 rad)]
2
=
0
.
993633
.
004
(part 1 oF 4) 10 points
A disk 3
.
46 cm in radius rotates at a constant
rate oF 1230 rev
/
min about its central axis.
Determine its angular speed in radians per
second.
Correct answer: 128
.
805 rad
/
s.
Explanation:
Convert the units From revolutions per min
utes to radians per second,
ω
=
ω
0
µ
2
π
rad
60 s
¶
.
The linear speed at
r
From the center oF the
disc is,
v
=
r ω
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View Full DocumentHusain, Zeena – Homework 8 – Due: Oct 21 2003, 4:00 am – Inst: H L Berk
2
If the radius of the disc is given by
R
, the
radial acceleration on the rim is,
a
r
=
R ω
2
The distance a point on the rim moves in time
t
is,
s
=
R θ
=
R ω t
005
(part 2 of 4) 10 points
Determine the linear speed at a point 1
.
8 cm
from its center.
Correct answer: 2
.
3185 m
/
s.
Explanation:
006
(part 3 of 4) 10 points
Determine the radial acceleration of a point
on the rim.
Correct answer: 574
.
043 m
/
s
2
.
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