Page 192 - Fisika Terapan for Engineers and Scientists

392 CHAPTER 12 Rotation of a Rigid Body

REVIEW PROBLEMS

75. An automobile has wheels of diameter 0.63 m. If the automo- form thickness, its mass is M, and its radius is R. Treat the
bile is traveling at 80 km/h, what is the instantaneous velocity spokes as thin rods of length R/2 and width R/12.
vector (relative to the ground) of a point at the top of the
wheel? At the bottom? At the front? R/2
76. The propeller of an airplane is turning at 2500 rev/min while the
airplane is cruising at 200 km/h.The blades of the propeller are
1.5 m long.Taking into account both the rotational motion of
the propeller and the translational motion of the aircraft, what is
the velocity (magnitude and direction) of the tip of the propeller?
77. An automobile accelerates uniformly from 0 to 80 km/h in 6.0
s.The automobile has wheels of radius 30 cm. What is the angu-
lar acceleration of the wheels? What is their final angular veloc-
ity? How many turns do they make during the 6.0-s interval? R FIGURE 12.31 A wheel.
78. The minute hand of a wall clock is a rod of mass 5.0 g and
*84. The total kinetic energy of a rolling body is the sum of its
length 15 cm rotating about one end. What is the rotational 2
1
translational kinetic energy Mv and its rotational kinetic
kinetic energy of the minute hand? 2 2
1
energy I
. Suppose that a cylinder, a sphere, and a pipe (a
2
79. What is the kinetic energy of rotation of a phonograph record
cylindrical shell) of equal masses 2.0 kg are rolling with equal
of mass 170 g and radius 15.2 cm rotating at 33 1 3 revolutions speeds of 1.0 m/s. What is the total kinetic energy of each?
per minute? To give this phonograph record a translational
*85. A uniform solid cylinder is initially at rest at the top of a ramp
kinetic energy of the same magnitude, how fast would you
of height 1.5 m. If the cylinder rolls down this ramp without
have to throw it?
slipping, what will be its speed at the bottom? (Hint: Use
80. The wheel of a wagon consists of a rim of mass 20 kg and energy conservation. The kinetic energy of the cylinder at the
eight spokes in the shape of rods of length 0.50 m and mass bottom of the ramp is the sum of its translational kinetic
1
1
0.80 kg each. energy Mv 2 and its rotational kinetic energy I
2 .)
2
2
(a) What is the moment of inertia of this wheel about its axle? **86. An airplane propeller (Fig. 12.32) is rotating at 3000 rev/min
(b) What is the kinetic energy of this wheel when rotating at when one of the blades breaks off at the hub. Treat the blade
1.0 rev/s? as a rod, of length 1.2 m. The blade is horizontal and swinging
upward at the instant it breaks.
*81. A solid body consists of two uniform solid spheres of mass M
and radius R welded together where they touch (see Fig. 12.30). (a) What is the velocity (magnitude and direction) of the
What is the moment of inertia of this rigid body about the motion of the center of mass of the blade immediately
longitudinal axis through the center of the spheres? About the after this instant?
transverse axis through the point of contact? (b) What is the angular velocity of the rotational motion of
the blade about its own center of mass?
(c) Suppose that this happens while the aircraft is on the
ground, with the hub of the propeller 2.4 m above the
ground. How high above the ground does the center of mass
R of the broken propeller blade rise? Neglect air resistance.
FIGURE 12.30 Two
connected solid spheres.

*82. A .22-caliber bullet is a solid cylinder of length 7.0 mm and
radius 2.7 mm capped at its front with a hemisphere of the
same radius. The mass of the bullet is 15 g.
(a) What is the moment of inertia of this bullet when rotat-
ing about its axis of symmetry?
(b) What is the rotational kinetic energy of the bullet when
3
rotating at 1.2 10 rev/s?
*83. Find the moment of inertia of the wheel shown in Fig. 12.31
rotating about its axis. The wheel is made of material of uni- FIGURE 12.32 An airplane propeller.