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Solutions to Assigned Problems, Unit 2, Chapter 5
CIRCULAR MOTION
1.
Strategy
Find the arc length swept out by the carnival swing.
Solution
Use Eq. (54).
2
r
a
d
(8.0 m)(120 )
17 m
360
sr
π
θ
⎛⎞
==
°
=
⎜⎟
°
⎝⎠
5.
Strategy
Use Eq. (59) to find the angular speed of the bicycle’s tires.
Solution
9.0 m s
26 rad s
0.35 m
v
r
ω
=
7.
(a)
Strategy and Solution
There are 2
radians per revolution and 60 seconds per minute, so
33.3 rev
2 rad
1 min
3.49 rad s .
min
rev
60 s
⎛
⎞
⎛
⎞
=
⎜
⎟
⎜
⎟
⎝
⎠
⎝
⎠
(b)
Strategy
Use the relationship between linear speed and angular speed.
Solution
Find the speed of the doll.
(0.13 m)(3.49 rad s)
0.45 m s
vr
=
13.
(a)
Strategy
Use the relationship between linear speed and radial acceleration.
Solution
The radius
r
is half the length of the rod.
2
2
rr
, so
(1.0 m)(980 m s )
31 m s .
v
av
r
a
r
=
=
(b)
Strategy
Use the relationship between angular speed and radial acceleration.
Solution
2
2r
r
980 m s
31 rad s .
1.0 m
a
ar
r
ωω
=
=
17.
(a)
Strategy
Use Newton’s second law and the relationship between linear speed and radial acceleration.
Solution
According to Newton’s second law,
22
2
, thus,
.
vv
m
v
FTm
am
m
T
rL
L
Σ==
=
=
=
(b)
Strategy
Draw a freebody diagram for the rock. Use Newton’s second law.
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View Full DocumentChapter 5:
Circular Motion
College Physics
2
Solution
Decompose the force into vertical (
y
) and radial (r) components.
2
rr
and
0.
yy
mv
FT
F Tm
g
L
Σ= =
Σ = − =
Find the magnitude of the tension.
2
2
22
2
r
()
y
mv
TT
T
m
g
L
⎛⎞
=+
=
+
⎜⎟
⎝⎠
Find the direction of the tension with respect to the horizontal.
2
11
1
2
r
tan
tan
tan
y
mv
L
T
mg
gL
T
v
θ
−−
−
==
=
m
g
T
y
19.
(a)
Strategy
Use Newton’s second law and the relationship between radial acceleration and linear speed.
Solution
2
rs
r
0, so
, and
.
y
v
FN
m
g
N
m
g
Ffm
am
R
Σ=− =
=
Σ== =
Find
v
.
2
ss
s
, so
.
v
f
mg
m
v
gR
R
μμ
=
(b)
Strategy
Consider the forces acting on the car.
Solution
Initially, the freebody diagram is
N
W
f
s
When the force of static friction becomes too small, the tires slip and the freebody diagram is
N
W
f
k
outside of the curve.
21.
Strategy
Let the
x
axis point toward the center of curvature and the
y
axis point upward. Draw a freebody
diagram. Use Newton’s second law and the relationship between radial acceleration and linear speed.
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 Fall '08
 ARIAS
 Circular Motion

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