lim (kl9356) – Practice Problems 1 – Weathers – (17104)
1
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79
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001
10.0 points
At
t
= 0, a wheel rotating about a fixed axis at
a constant angular deceleration of 0
.
75 rad
/
s
2
has an angular velocity of 3
.
3 rad
/
s and an
angular position of 6
.
3 rad.
What is the angular position of the wheel
after 3 s? Answer in units of rad.
002
10.0 points
A student throws a long stick of length
0
.
11 m and mass 0
.
5 kg into the air in such
a way that the center of mass rises vertically.
At the moment it leaves his hand, the stick
is horizontal and the speed of the end of the
stick nearest to him is zero. When the center
of mass of the stick reaches its highest point,
the stick is horizontal, and it has made 21
complete revolutions.
0
.
055 m
0
.
11 m
v
cm
0
0
.
5 kg
v
end
0
How long did it take for the center of mass
to reach its highest point? Assume the stick’s
cross sectional area and mass is uniform. The
acceleration of gravity is 9
.
8 m
/
s
2
.
Answer in units of s.
003
10.0 points
A tire placed on a balancing machine in a ser
vice station starts from rest and turns through
5
.
42 rev in 0
.
6 s before reaching its final an
gular speed.
Find its angular acceleration.
Answer in
units of rad
/
s
2
.
004
10.0 points
The angular position of an object that rotates
about a fixed axis is given by
θ
(
t
) =
θ
0
e
βt
,
where
β
= 3 s
−
1
,
θ
0
= 1
.
3 rad, and
t
is in
seconds.
What is the magnitude of the total linear
acceleration at
t
= 0 of a point on the object
that is 2 cm from the axis? Answer in units of
cm
/
s
2
.
005
(part 1 of 4) 10.0 points
A disk 5
.
2 cm in radius rotates at a constant
rate of 1070 rev
/
min about its central axis.
Determine its angular speed in radians per
second. Answer in units of rad
/
s.
006
(part 2 of 4) 10.0 points
Determine the linear speed at a point 1
.
86 cm
from its center. Answer in units of m
/
s.
007
(part 3 of 4) 10.0 points
Determine the radial acceleration of a point
on the rim. Answer in units of m
/
s
2
.
008
(part 4 of 4) 10.0 points
Determine the total distance a point on the
rim moves in 2
.
83 s. Answer in units of m.
009
10.0 points
The center of mass of a pitched baseball or
radius 3
.
03 cm moves at 25 m
/
s.
The ball
spins about an axis through its center of mass
with an angular speed of 183 rad
/
s.
Calculate the ratio of the rotational energy
to the translational kinetic energy. Treat the
ball as a uniform sphere.
010
10.0 points
The hour and minute hands of a tower clock
like Big Ben in London are 2
.
76 m and 4
.
49 m
long and have masses of 60
.
5 kg and 105 kg,
respectively.
Calculate the total rotational kinetic en
ergy of the two hands about the axis of ro
tation.
Model the hands as long thin rods.
Answer in units of J.
011
10.0 points
The length of each of the bonds between
the atoms of a molecule of nitrogen (N
2
) is
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lim (kl9356) – Practice Problems 1 – Weathers – (17104)
2
0
.
103 nm.
The mass of a nitrogen atom is
2
.
32
×
10
−
11
pg.
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 Fall '08
 Weathers
 Magnetism, Mass, Moment Of Inertia, Rotation, lim

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