homework 09 – VENNES, ROSS – Due: Nov 2 2007, 1:00 am
1
Question 1, chap 12, sect 2.
part 1 of 2
10 points
A
record
has
an
angular
speed
of
44
.
2 rev
/
min.
What is its angular speed?
Correct answer: 4
.
62862 rad
/
s (tolerance
±
1 %).
Explanation:
1 rev = 6
.
28319 rad, and
1 min = 60 s
,
Therefore,
ω
1
= (44
.
2 rev
/
min)
parenleftbigg
2
π
rad
rev
parenrightbigg parenleftbigg
1 min
60 s
parenrightbigg
= 4
.
62862 rad
/
s
.
Question 2, chap 12, sect 2.
part 2 of 2
10 points
Through what angle, in radians, does it
rotate in 1
.
41 s?
Correct answer: 6
.
52635 rad (tolerance
±
1
%).
Explanation:
θ
=
ω t
= (4
.
62862 rad
/
s) (1
.
41 s)
= 6
.
52635 rad
.
Question 3, chap 12, sect 2.
part 1 of 2
10 points
A racing car travels on a circular track of
radius 335 m. The car moves with a constant
linear speed of 42
.
4 m
/
s.
Find its angular speed.
Correct answer: 0
.
126567 rad
/
s (tolerance
±
1 %).
Explanation:
The linear speed
v
and the angular speed
ω
are related by,
v
=
R ω
⇒
ω
=
v
R
.
Question 4, chap 12, sect 2.
part 2 of 2
10 points
Find the magnitude of its acceleration.
Correct answer: 5
.
36645 m
/
s
2
(tolerance
±
1
%).
Explanation:
If the car is moving at a constant speed,
there is no tangential acceleration, thus the
acceleration is purely radial,
a
r
=
v
2
R
.
Question 5, chap 12, sect 2.
part 1 of 1
10 points
A woman passes through a revolving door
with a tangential speed of 1.8 m/s.
If she is 0.78 m from the center of the door,
what is the door’s angular speed?
Correct answer: 2
.
30769 rad
/
s (tolerance
±
1 %).
Explanation:
Basic Concept:
v
t
=
rω
Given:
v
t
= 1
.
8 m
/
s
r
= 0
.
78 m
Solution:
ω
=
v
t
r
=
1
.
8 m
/
s
0
.
78 m
= 2
.
30769 rad
/
s
Question 6, chap 12, sect 2.
part 1 of 1
10 points
The speed of a moving bullet can be deter
mined by allowing the bullet to pass through
two rotating paper disks mounted a distance
64
.
5 cm apart on the same axle.
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homework 09 – VENNES, ROSS – Due: Nov 2 2007, 1:00 am
2
angular displacement 48
◦
of the two bullet
holes in the disks and the rotational speed
866 rev
/
min of the disks, we can determine
the speed
v
of the bullet.
48
◦
v
866 rpm
64
.
5 cm
What is the speed of the bullet?
Correct answer: 69
.
8212 m
/
s (tolerance
±
1
%).
Explanation:
Let :
ω
= 866 rev
/
min
,
d
= 64
.
5 cm
,
and
θ
= 48
◦
.
From
θ
=
ω t
the time to pass through an
angle
θ
is
t
=
θ
ω
=
(48
◦
)
(90
.
6873 rad
/
s)
π
rad
180
◦
= 0
.
00923788 s
.
Then the speed of the bullet is
v
=
d
t
=
(64
.
5 cm) (0
.
01 m
/
cm)
0
.
00923788 s
= 69
.
8212 m
/
s
.
Question 7, chap 12, sect 2.
part 1 of 3
10 points
A car accelerates uniformly from rest and
covers a distance of 53 m in 6
.
9 s.
If the
diameter
of a tire is 49 cm, find the
angular acceleration of the wheel.
Correct answer: 9
.
08744 rad
/
s
2
(tolerance
±
1 %).
Explanation:
Find the wheel’s linear acceleration
x
=
1
2
a t
2
⇒
a
=
2
x
t
2
.
Then, angular acceleration is
α
=
a
R
=
2
x
R t
2
=
2 (53 m)
1
2
(49 cm) (6
.
9 s)
2
= 9
.
08744 rad
/
s
2
,
where
x
is the distance traveled,
t
is the time
taken and
R
=
1
2
(49 cm) is the radius of the
wheel.
Question 8, chap 12, sect 2.
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 Kinetic Energy, Work, Moment Of Inertia, Correct Answer

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