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MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

        1) At time t = 0 s, a wheel has an angular displacement of zero radians and an angular velocity of            1)
           +18 rad/s. The wheel has a constant acceleration of -0.55 rad/s2 . In this situation, the time t (after
           t = 0 s), at which the kinetic energy of the wheel is twice the initial value, is closest to:
              A) 69 s                B) 46 s             C) 57 s                 D) 79 s                 E) 33 s

        2) A small mass is placed on a record turntable that is rotating at 45 rpm. The acceleration of the mass      2)
           is
              A) greater the farther the mass is from the center.
              B) independent (in magnitude) of the position of the mass on the turntable.
              C) directed perpendicular to the line joining the mass and the center of rotation.
              D) greater the closer the mass is to the center.
              E) zero.

                                                             Figure 9.1




Point P is on the rim of a wheel of radius 2.0 m. At time t = 0, the wheel is at rest, and P is on the x-axis. The wheel
undergoes a uniform angular acceleration of 0.01 rad/s2 about the center O.

        3) In Fig. 9.1, the magnitude of the acceleration of P, when it reaches the y-axis, is closest to:            3)
              A) 0.075 m/s2        B) 0.066 m/s2         C) 0.072 m/s2        D) 0.063 m/s2           E) 0.069 m/s2

        4) At any angular speed, a certain uniform solid sphere of diameter D has half as much rotational             4)
           kinetic energy as a certain uniform thin-walled hollow sphere of the same diameter when both are
           spinning about an axis through their centers. If the mass of the solid sphere is M, the mass of the
           hollow sphere is:
             A) 5/6 M               B) 3/5 M           C) 2 M                 D) 5/3 M              E) 6/5 M

        5) In rotational dynamics, moment of inertia plays a role analogous to one of the quantities                  5)
           encountered in linear motion, namely
              A) translational kinetic energy.
              B) momentum.
              C) impulse.
              D) mass.
              E) a "couple" or "moment" of a force.




                                                                  1
                                                   Figure 10.1




6) A light triangular plate OAB is in a horizontal plane. Three forces, F1 = 3 N, F2 = 1 N, and F3 = 9 N,   6)
  act on the plate, which is pivoted about a vertical axes through point O. In Fig. 10.1, the moment
  arm of force F1 about the axis through point O is closest to:
     A) 1.4 N · m          B) 0.90 N · m        C) 1.8 N · m          D) 1.6 N · m          E) 1.1 N · m


7) A drum has a radius of 0.40 m and a moment of inertia of 4.7 kg · m2. The frictional torque of the       7)
   drum bearings is 3.0 N · m. A ring at one end of a rope is slipped on a short peg on the rim of the
   drum, and a 20-m length of rope is wound upon it. The drum is initially at rest. A constant force is
   applied to the free end of the rope until the rope is completely unwound and slips off the peg. At
   that instant, the angular velocity of the drum is 16 rad/s. The drum then decelerates and comes to a
   halt. In this situation, the constant force applied to the rope is closest to:
     A) 23 N                  B) 7.5 N             C) 30 N               D) 38 N           E) 15 N

8) A uniform solid cylindrical log begins rolling without slipping down a ramp that rises 28.0° above       8)
   the horizontal. After it has rolled 4.20 m along the ramp, the magnitude of its linear acceleration is
   closest to:
      A) 4.60 m/s2           B) 3.07 m/s2         C) 2.30 m/s2       D) 9.80 m/s2           E) 3.29 m/s2




                                                        2
                                                            Figure 10.2




A wheel has a radius of 0.40 m and is mounted on frictionless bearings. A block is suspended from a ropethat is wound on
the wheel and attached to it. The wheel is released from rest and the block descends 1.5 m in 2.00 s. The tension in the rope
during the descent of the block is 20 N.

        9) In Fig. 10.2 the moment of inertia of the wheel is closest to:                                          9)
              A) 3.5 kg · m2
             B) 3.7 kg · m2
             C) 4.1 kg · m2
             D) 4.3 kg · m2
             E) 3.9 kg · m2

                                                            Figure 10.6




The radius of a 3.0-kg wheel is 6.0 cm. The wheel is released from rest at point A on a 30° incline. The wheel rolls without
slipping and moves 2.4 m to point B in 1.20 s.

      10) In Fig. 10.6, the angular acceleration of the wheel is closest to:                                       10)
             A) 65 rad/s2          B) 82 rad/s2          C) 56 rad/s2          D) 73 rad/s2       E) 48 rad/s2




                                                                 3
                                                     Figure 10.8




11) In Fig. 10.8, a carousel has a radius of 3.0 m and a moment of inertia of 8000 kg· m2 . The carousel is    11)
    rotating unpowered and without friction with an angular velocity of 1.2 rad/s. An 80-kg man runs
    with a velocity of 5.0 m/s, on a line tangent to the rim of the carousel, overtaking it. The man runs
    onto the carousel and grabs hold of a pole on the rim. The change in the angular velocity of the
    carousel is closest to:
       A) +0.06 rad/s
       B) +0.04 rad/s
       C) +0.08 rad/s
       D) -0.05 rad/s
       E) -0.07 rad/s

12) Which of the following is an accurate statement?                                                           12)
     A) A particle moving in a straight line with constant speed necessarily has zero angular
        momentum.
     B) The angular momentum of a moving particle depends on the specific origin with respect to
        which the angular momentum is calculated.
     C) If the speed of a particle is constant, then the angular momentum of the particle about any
        specific origin must also be constant.
     D) Consider a planet moving in a circular orbit about a star. Even if the planet is spinning it is
        not possible for its total angular momentum to be zero.
     E) If the torque acting on a particle is zero about an arbitrary origin, then the angular
        momentum of the particle is also zero about that origin.

13) A uniform disk has a mass of 2.6 kg and a radius of 0.75 m. The disk is mounted on frictionless            13)
    bearings and is used as a turntable. The turntable is initially rotating at 60 rpm. A thin-walled
    hollow cylinder has the same mass and radius as the disk. It is released from rest, just above the
    turntable, and on the same vertical axis. The hollow cylinder slips on the turntable for 0.20 s until it
    acquires the same final angular velocity as the turntable. The loss of kinetic energy of the system is
    closest to:
       A) 9.6 J             B) 11 J              C) 8.1 J                D) 4.9 J             E) 6.5 J




                                                          4
14) In an interesting lecture demonstration a student sits in a swivel chair holding a spinning bicycle       14)
    wheel oriented with its axis vertical. Initially the chair is motionless. Now the student rotates the
    axis of the spinning wheel by 180°, so that it is again vertical, but now the wheel is spinning in the
    opposite sense with respect to the room. When this is done the student and chair begin to rotate
    also. Which of the following is an accurate statement concerning this process?
       A) In the final state the chair will be rotating in the opposite sense of the wheel, but at a much
          higher frequency.
       B) Angular momentum, but not angular kinetic energy, is conserved in this process,
          independent of whether or not friction is present.
       C) In the final state the chair will be rotating in the same sense as the wheel, but at a much lower
          frequency.
       D) Angular velocity is conserved in this process.
       E) Assuming the swivel bearing of the chair is frictionless, angular kinetic energy is conserved in
          this process.

15) A bicycle wheel of radius 0.36 m and mass 3.20 kg is set spinning at 4.00 rev/s. A bolt is attached to    15)
    extend the axle in length, and a string is attached to the axle at a distance of 0.10 m from the wheel.
    Initially the axle of the spinning wheel is horizontal, and the wheel is suspended only from the
    string. At what rate will the wheel process about the vertical?
       A) 18 rpm               B) 0.30 rpm         C) 0.77 rpm           D) 2.9 rpm            E) 1.9 rpm




                                                         5
      
 1)  D 
      
 2)  A 
      
 3)  B 
      
 4)  E 
      
 5)  D 
      
 6)  D 
      
 7)  D 
      
 8)  B 
      
 9)  D 
      
10)  C 
      
11)  B 
      
12)  B 
      
13)  A 
      
14)  B 
      
15)  D 

				
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