bello (rtb473) – hw8 – Demkov – (59910)
1
This printout
should have 47 questions.
Multiplechoice questions may continue on
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before answering.
001
(part 1 of 3) 10.0 points
A beetle takes a joy ride on a pendulum. The
string supporting the mass of the pendulum
is 181 cm long.
If the beetle rides through a swing of 39
◦
,
how far has he traveled along the path of the
pendulum?
Correct answer: 123
.
203 cm.
Explanation:
Arc length is defined as
s
=
r θ
= (181 cm)(39
◦
)
·
parenleftBig
π
180
◦
parenrightBig
= 123
.
203 cm
,
002
(part 2 of 3) 10.0 points
What is the displacement experienced by the
beetle while moving theough the same angle
39
◦
?
Correct answer: 120
.
838 cm.
Explanation:
Using the law of cosines, we have
bardbl
vector
R
bardbl
=
radicalbig
r
2
+
r
2
−
2
r r
cos
θ
=
r
radicalbig
2 (1
−
cos
θ
)
= (181 cm)
radicalbig
2(1
−
cos 39
◦
)
= 120
.
838 cm
.
Alternative Solution:
Divide the isosce
les triangle in half. Then
bardbl
vector
R
bardbl
= 2
.
0
r
sin
parenleftbigg
θ
2
parenrightbigg
= 2
.
0 (181 cm)(sin 19
.
5
◦
)
= 120
.
838 cm
.
003
(part 3 of 3) 10.0 points
If the pendulum at some instant is swinging
at 2
.
5 rad
/
s, how fast is the beetle traveling?
Correct answer: 452
.
5 cm
/
s.
Explanation:
Linear and angular velocity are related by
v
=
r ω
= (181 cm)(2
.
5 rad
/
s)
= 452
.
5 cm
/
s
.
keywords:
004
10.0 points
A large wheel is coupled to a wheel with half
the diameter as shown.
r
2
r
How
does
the
rotational
speed
of
the
smaller wheel compare with that of the larger
wheel?
How do the tangential speeds at
the rims compare (assuming the belt doesn’t
slip)?
1.
The smaller wheel has four times the ro
tational speed and the same tangential speed
as the larger wheel.
2.
The smaller wheel has twice the rotational
speed and twice the tangential speed as the
larger wheel.
3.
The smaller wheel has half the rotational
speed and half the tangential speed as the
larger wheel.
4.
The smaller wheel has twice the rotational
speed and the same tangential speed as the
larger wheel.
correct
Explanation:
v
=
r ω
The tangential speeds are equal, since the
rims are in contact with the belt and have the
same linear speed as the belt.
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bello (rtb473) – hw8 – Demkov – (59910)
2
The smaller wheel (with half the radius)
rotates twice as fast:
parenleftbigg
1
2
r
parenrightbigg
(2
ω
) =
r ω
=
v
005
10.0 points
A phonograph record has an initial angular
speed of 10 rev/min. The record slows to 1.4
rev/min in 37 s.
What is the record’s average angular accel
eration during this time interval?
Correct answer:
−
1
.
27991 rad
/
s
2
.
Explanation:
Let :
ω
o
= 10 rev
/
min
,
ω
f
= 1
.
4 rev
/
min
,
and
Δ
t
= 37 s
.
α
avg
=
ω
f
−
ω
o
Δ
t
=
14 rev
/
min
−
36 rev
/
min
1
.
8 s
×
2
π
rad
1 rev
·
1 min
60 s
=
−
1
.
27991 rad
/
s
2
.
keywords:
006
10.0 points
A mass attached to a 46.1 cm string starts
from rest and is rotated in a circular path
exactly 56 times in 1.15 min before reaching a
final angular speed.
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 Spring '07
 Swinney
 mechanics, Angular Momentum, Kinetic Energy, Moment Of Inertia, Correct Answer, Bello

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