Homework: Week 9 – Chapter 10 – SOLUTIONS
1.
(106) A spot of paint on a bicycle tire moves in a circular path of radius 0.38 m. When the spot has
traveled a linear distance of 1.50 m, through what angle has the tire rotated? Give your answer in
radians.
SOLUTION
1.50m
3.9rad
0.38m
s
r
θ
==
=
2.
(1015) The angular speed of a propeller on a boat increases with constant acceleration from 12 rad/s
to 26 rad/s in 2.5 seconds. Through what angle did the propeller turn during this time?
SOLUTION
0
11
(
)
(12 rad/s
26 rad/s)(2.5 s)
48 rad
22
t
θω
ω
∆=
+
=
+
=
3.
(1018) A discus thrower starts from rest and begins to rotate with a constant angular acceleration of
(a)
How many revolutions does it take for the discus thrower’s angular speed to reach 6.3 rad/s?
(b)
How long does this take?
SOLUTIONS
(a)
2
..
rad / s
()
2
2
2
00
2
2
0
0
2
2
rad
s
rad
s
2(
)
2
6.3
0
2.2
1 rev
(18.0 rad)
2
r
a
d
2.9 rev
ωω
α
θθ
π
=+ −
−
−=
−
=
⎛⎞
=
⎜⎟
⎝⎠
=
(b)
2
0
rad
0s
rad
s
6.3
0
2.9 s
2.2
t
t
ωα
=+
−
−
=
4.
(1028) A carousel at the local carnival rotates once every 45 seconds.
(a)
What is the linear speed of an outer horse on the carousel, which is 2.75 m from the axis of
rotation?
(b)
What is the linear speed of an inner horse, which is 1.75 m from the axis of rotation?
SOLUTIONS
(a)
t
1 rev
2
rad
(2.75 m)
0.38 m/s
45 s
rev
vr
⎛
⎞
=
⎜
⎟
⎝
⎠
(b)
t
1 rev
2
rad
(1.75 m)
0.24 m/s
45 s
rev
v
⎛
⎞
⎜
⎟
⎝
⎠
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(1030) Jeff of the Jungle swings on a vine that is 7.2 m long. At some point in his swing, Jeff's angular
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 Fall '09
 WOODAHL
 Physics, Acceleration, Work, Moment Of Inertia, Rotation, m1 gh

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