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Lesson 9 Homework Solutions
1.
What is the arc length subtended by an angle of
π
/4 rad on a circle of
radius 50 cm?
R = 50 cm = 0.5 m,
θ
=
π
/4 rad.
The arc length s that subtends an
angle
θ
radians at the center of a
circle of radius r is given by:
s = r
θ
= 0.5
×
π
/4 =
π
/8 m
r
r
θ
s
2.
What is the degree measure of an angle
π
/9?
Since
π
radians contain 180
o
,
π
/9 radians contain:
180
0
9
2
o
π
×=
3.
What is the radian measure of an angle 130
o
?
130
130
18
1
8
0
3
1
o
=×
=
4.
A satellite in a circular orbit has a period of 10 hours. What is its
frequency in revolutions per day?
Period T = 10 h = 10/24 day = 5/12 day
Frequency and period are reciprocal of each other.
12
per da
1
12
5
1
5
y
f
T
==
=
5.
The blades of a helicopter rotor describe an angle of 14
π
rad each
second. (i) What is the angular speed of the rotor in rpm? (ii) If the
length of a blade is 2.3 m, what is the linear speed of the tip of a
blade?
(i)
The angle described in one minute = 14
π
× 60 = 840
π
rad
The number of revolutions in one minute is:
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8
2
40
0m
2
rp
π
=
(ii)
Angular velocity
ω
= 14
π
rads
1
A point at the edge of a blade describes a circle of radius r = 2.3
m. Its linear speed v is given by:
v
=
r
ω
= 2.3 m
×
14
π
rad s
1
=
101.2 ms
1
6.
A 0.5kg stone tied to a 1.2 m string is whirled in a horizontal circle
so that the radius of the circle is the same as the length of the string.
(a)
Express the speed of the stone in terms of the radius (r) of the
circle and the frequency (f)
of revolution.
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This note was uploaded on 05/01/2011 for the course PHY 2048 taught by Professor George during the Fall '10 term at Edison State College.
 Fall '10
 George
 Physics, Work

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