Page 187 - Fisika Terapan for Engineers and Scientists

Problems 387

4. In an experiment at the Oak Ridge Laboratory, a carbon fiber angular velocity is 50 radians/s, what is the corresponding
disk of 0.70 m in diameter was set spinning at 37000 rev/min. total acceleration of the point?
What was the speed at the edge of this disk? 13. The angular position of a ceiling fan during the first two sec-
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5. The rim of a phonograph record is at a distance of 15 cm from onds after start-up is given by C[t (t /4 s)], where
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the center, and the rim of the paper label on the record is at a C 20/s and t is in seconds. What are the angular position,
distance of 5 cm from the center. angular frequency, and angular acceleration at t 0 s? At
(a) When this record is rotating at 33 1 3 rev/min, what is the t 1.0 s? At t 2.0 s?
translational speed of a point on the rim of the record? *14. An aircraft passes directly over you with a speed of 900 km/h
The translational speed of a point on the rim of the paper at an altitude of 10000 m. What is the angular velocity of the
label? aircraft (relative to you) when directly overhead? Three
(b) What are the centripetal accelerations of these points? minutes later?
6. An electric drill rotates at 5000 rev/min. What is the frequency *15. The outer edge of the grooved area of a long-playing record is
of rotation (in rev/s)? What is the time for one revolution? at a radial distance of 14.6 cm from the center; the inner edge
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What is the angular velocity (in radians/s)? is at a radial distance of 6.35 cm. The record rotates at 33 3
rev/min. The needle of the pickup arm takes 25 min to play
7. An audio compact disk (CD) rotates at 210 rev/min when
the record, and in that time interval it moves uniformly and
playing an outer track of radius 5.8 cm. What is the angular
radially from the outer edge to the inner edge. What is the radial
velocity in radians/s? What is the tangential speed of a point
speed of the needle? What is the speed of the outer edge relative
on the outer track? Because the CD has the same linear
to the needle? What is the speed of the inner edge relative to
density of bits on each track, the drive maintains a constant
the needle?
tangential speed. What is the angular velocity (in radians/s)
when playing an inner track of radius 2.3 cm? What is the *16. Consider the phonograph record described in Problem 15. What
corresponding rotational frequency (in rev/s)? is the total length of the groove in which the needle travels?
8. An automobile travels one-fourth of the way around a traffic
circle in 4.5 s. The diameter of the traffic circle is 50 m. The 12.3 Motion with Constant
automobile travels at constant speed. What is that speed? Angular Acceleration
What is the angular velocity in radians/s?
9. When a pottery wheel motor is switched on, the wheel accel- 17. The blade of a circular saw of diameter 20 cm accelerates uni-
erates from rest to 90 rev/min in 5.0 s. What is its angular formly from rest to 7000 rev/min in 1.2 s. What is the angular
velocity at t 5.0 s (in radians/s)? What is the linear speed acceleration? How many revolutions will the blade have made
of a piece of clay 10 cm from the center of the wheel at by the time it reaches full speed?
t 5.0 s? What is its average angular acceleration during the 18. A large ceiling fan has blades of radius 60 cm. When you switch
acceleration? this fan on, it takes 20 s to attain its final steady speed of
10. A grinding wheel of radius 6.5 cm accelerates from rest to its 1.0 rev/s. Assume a constant angular acceleration.
operating speed of 3450 rev/min in 1.6 s. When up to speed, (a) What is the angular acceleration of the fan?
what is its angular velocity in radians/s? What is the linear (b) How many revolutions does it make in the first 20 s?
speed at the edge of the wheel? What is its average angular
(c) What is the distance covered by the tip of one blade in the
acceleration during this 1.6 s? When turned off, it decelerates
first 20 s?
to a stop in 35 s. What is its average angular acceleration
during this time? 19. When you switch on a PC computer, the disk in the disk drive
takes 5.0 s to reach its final steady speed of 7200 rev/min.
11. When drilling holes, manufacturers stay close to a recom-
What is the average angular acceleration?
mended linear cutting speed in order to maintain efficiency
while avoiding overheating. The rotational speed of the drill 20. When you turn off the motor, a phonograph turntable initially
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thus depends on the diameter of the hole. For example, rec- rotating at 33 3 rev/min makes 25 revolutions before it stops.
ommended linear cutting speeds are typically 20 m/min for Calculate the angular deceleration of this turntable; assume it
steel and 100 m/min for aluminum. What is the corresponding is constant.
rotational rate (in rev/s) when drilling a 3.0-mm-diameter 21. A large merry-go-round rotates at one revolution each
hole in aluminum? When drilling a 2.5-cm-diameter hole 9.0 seconds. When shut off, it decelerates uniformly to a stop
in steel? in 16 s. What is the angular acceleration? How many revolu-
12. An electric blender accelerates from rest to 500 radians/s in tions does the merry-go-round make during the deceleration?
0.80 s. What is the average angular acceleration? What is the 22. A cat swipes at a spool of thread, which then rolls across the
corresponding average tangential acceleration for a point on floor with an initial speed of 1.0 m/s. The spool decelerates
the tip of a blender blade a distance 3.0 cm from the axis? If uniformly to a stop 3.0 m from its initial position. The spool
this point has that tangential acceleration when the blender’s has a radius of 1.5 cm and rolls without slipping. What is the