Page 189 - Fisika Terapan for Engineers and Scientists

Problems 389

36. The water molecule has a shape shown in Fig. 12.21.The *45. Suppose that a supertanker transports 4.4 10 kg of oil from
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distance between the oxygen and the hydrogen atoms is d, and a storage tank in Venezuela (latitude 10 north) to a storage
the angle between the hydrogen atoms is . From spectroscopic tank in Holland (latitude 53 north). What is the change of
investigations it is known that the moment of inertia of the mol- the moment of inertia of the Earth–oil system?
2
ecule is 1.93 10 47 kg m for rotation about the axis AA
and *46. A dumbbell consists of two uniform spheres of mass M and
2
1.14 10 47 kg . m for rotation about the axis BB
. From this
radius R joined by a thin rod of mass m. The distance between
information and the known values of the masses of the atoms,
the centers of the sphers is l (Fig. 12.22). What is the moment
determine the values of d and .Treat the atoms as pointlike.
of inertia of this device about an axis through the center of the
rod perpendicular to the rod? About an axis along the rod?
B'
H
d
R

A O A'
O
R l
d
H
FIGURE 12.22 A dumbbell.
B
FIGURE 12.21 Atoms in a water molecule.
*47. Suppose that the Earth consists of a spherical core of mass
0.22M and radius 0.54R and a surrounding mantle
E
E
37. What is the moment of inertia (about the axis of symmetry) of (a spherical shell) of mass 0.78M and outer radius R .
E
E
a bicycle wheel of mass 4.0 kg, radius 0.33 m? Neglect the Suppose that the core is of uniform density and the mantle is
mass of the spokes. also of uniform density. According to this simple model, what
38. An airplane propeller consists of three radial blades, each of is the moment of inertia of the Earth? Express your answer as
2
length 1.2 m and mass 6.0 kg. What is the kinetic energy of a multiple of M R .
E
E
this propeller when rotating at 2500 rev/min? Assume that *48. In order to increase her moment of inertia about a vertical
each blade is (approximately) a uniform rod. axis, a spinning figure skater stretches her arms out horizon-
39. Estimate the moment of inertia of a human body spinning rigidly tally; in order to reduce her moment of inertia, she brings her
about its longitudinal axis. Treat the body as a uniform cylin- arms down vertically along her sides. Calculate the change of
der of mass 70 kg, length 1.7 m, and average diameter 23 cm. moment of inertia between these two configurations of the
40. Use the parallel-axis theorem to determine the moment of inertia arms. Assume that each arm is a thin, uniform rod of length
of a solid disk or cylinder of mass M and radius R rotating about 0.60 m and mass 2.8 kg hinged at the shoulder a distance of
an axis parallel to its symmetry axis but tangent to its surface. 0.20 m from the axis of rotation.
41. The moment of inertia of the Earth is approximately *49. Find the moment of inertia of a thin rod of mass M and
2
0.331M R (see also Problem 34). Calculate the rotational length L about an axis through the center inclined at an angle
E
E
kinetic energy of the Earth. with respect to the rod.
42. Assume that a potter’s kickwheel is a disk of radius 60 cm and *50. Given that the moment of inertia of a sphere about a diameter
2
2
mass 120 kg. What is its moment of inertia? What is its rota- is MR , show that the moment of inertia about an axis tan-
5
2
7
tional kinetic energy when revolving at 2.0 rev/s? gent to the surface is MR .
5
43. A flywheel energy-storage system designed for the International *51. Find a formula for the moment of inertia of a uniform thin
Space Station has a maximum rotational rate of 53000 rev/min. square plate (mass m, dimension l l ) rotating about an axis
The cylindrical flywheel has a mass of 75 kg and a radius of 16 that coincides with one of its edges.
cm. For simplicity, assume the cylinder is solid and uniform. *52. A conical shell has mass M, height h, and base radius R.
What is the moment of inertia of the flywheel? What is the Assume it is made from a thin sheet of uniform thickness.
maximum rotational kinetic energy stored in the flywheel? What is its moment of inertia about its symmetry axis?
*44. An empty beer can has a mass of 15 g, a length of 12 cm, and *53. Suppose a peach of radius R and mass M consists of a spheri-
a radius of 3.3 cm. Find the moment of inertia of the can cal pit of radius 0.50R and mass 0.050M surrounded by a
about its axis of symmetry. Assume that the can is a perfect spherical shell of fruit of mass 0.95M. What is the moment of
cylinder of sheet metal with no ridges, indentations, or holes. inertia of the peach?