Exam Name___________________________________ 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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