第 1 頁, 共 7 頁 Chap10 1. Test Bank, Question 3 One revolution per minute is about: 0.0524 rad/s 0.105 rad/s 0.95 rad/s 1.57 rad/s 6.28 rad/s 2. *Chapter 10, Problem 8 The angular acceleration of a wheel is α = 5.0t 4 4.0t 2, with α in radians per second-squared and t in seconds. At time t = 0, the wheel has an angular velocity of +3 rad/s and an angular position of +8 rad. Write expressions for (a) the angular velocity (rad/s) and (b) the angular position (rad) as functions of time (s). Number 1 t 5-1.333333333333 t 3 + 3 Units rad/s Number 0.166666666667 t 6-0.333333333333 t 4 + 3 t+ 8 Units rad 3. Test Bank, Question 11 If the angular velocity vector of a spinning body points out of the page then, when viewed from above the page, the body is spinning: clockwise about an axis that is perpendicular to the page counterclockwise about an axis that is perpendicular to the page about an axis that is parallel to the page about an axis that is changing orientation about an axis that is getting longer 4. Test Bank, Question 12 The angular velocity vector of a spinning body points out of the page. If the angular acceleration vector points into the page then: the body is slowing down the body is speeding up the body is starting to turn in the opposite direction

第 2 頁, 共 7 頁 the axis of rotation is changing orientation none of the above 5. Test Bank, Question 29 A wheel of diameter 3.0 cm has a 4.0 m cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 2 rad/s 2. The cord will unwind in: 0.82 s 2.0 s 8.0 s 16 s 130 s 6. Test Bank, Question 31 A car travels north at constant velocity. It goes over a piece of mud which sticks to the tire. The initial acceleration of the mud, as it leaves the ground, is: vertically upward horizontally to the north horizontally to the south zero upward and forward at 45 to the horizontal 7. *Chapter 10, Problem 22 An astronaut is being tested in a centrifuge. The centrifuge has a radius of 7.5 m and, in starting, rotates according to θ = 0.32t 2, where t is in seconds and θ is in radians. When t = 6.0 s, what are the magnitudes of the astronaut's (a) angular velocity, (b) linear velocity, (c) tangential acceleration, and (d) radial acceleration? (a) Number 3.84 Units rad/s (b) Number 28.8 Units m/s (c) Number 4.8 Units m/s^2 (d) Number 110.592 Units m/s^2 8. Test Bank, Question 75 A small disk of radius R 1 is fastened coaxially to a larger disk of radius. The combination is free to rotate on a fixed axle, which is perpendicular to a horizontal frictionless table top, as shown in the overhead veiw below. The rotational

第 3 頁, 共 7 頁 inertia of the combination is I. A string is wrapped around the larger disk and attached to a block of mass m, on the table. Another string is wrapped around the smaller disk and is pulled with a force as shown. The tension in the string pulling the block is: R 1 F/ F/(I m 2 ) F/(I + m 2 ) F/(I ) F/(I + ) 9. Test Bank, Question 43 A pulley with a radius of 3.0 cm and a rotational inertia of 4.5 10 3 kg m 2 is suspended from the ceiling. A rope passes over it with a 2.0-kg block attached to one end and a 4.0-kg block attached to the other. The rope does not slip on the pulley. At any instant after the blocks start moving the object with the greatest kinetic energy is: the heavier block the lighter block the pulley either block (the two blocks have the same kinetic energy) none (all three objects have the same kinetic energy) 10. Test Bank, Question 47 The rotational inertia of a thin cylindrical shell of mass M, radius R, and length L about its central axis (X - X') is: M /2 ML 2 /2

第 4 頁, 共 7 頁 ML 2 M none of these 11. Test Bank, Question 54 The rotational inertia of a disk about its axis is 0.70 kg the axis, the rotational inertia becomes: m 2. When a 2.0 kg weight is added to its rim, 0.40 m from 0.38 kg m 2 0.54 kg m 2 0.70 kg m 2 0.86 kg m 2 1.0 kg m 2 12. *Chapter 10, Problem 40 Figure 10-33 shows an arrangement of 15 identical disks that have been glued together in a rod-like shape of length L = 1.6400 m and (total) mass M = 200.0 mg. The arrangement can rotate about a perpendicular axis through its central disk at point O. (a) What is the rotational inertia of the arrangement about that axis? Give your answer to four significant figures. (b) If we approximated the arrangement as being a uniform rod of mass M and length L, what percentage error would we make in using the formula in Table 10-2e to calculate the rotational inertia? Fig. 10-33 Problem 40. (a) Number 0.000044926281 Units kg m^2 (b) Number -0.221729490022 Units percent 13. *Chapter 10, Problem 44 Four identical particles of mass 0.764 kg each are placed at the vertices of a 4.54 m x 4.54 m square and held there by four massless rods, which form the sides of the square. What is the rotational inertia of this rigid body about an axis that (a) passes through the midpoints of opposite sides and lies in the plane of the square, (b) passes through the midpoint of one of the sides and is perpendicular to the plane of the square, and (c) lies in the plane of the square and passes through two diagonally opposite particles? (a) Number 15.7472624 Units kg m^2

第 5 頁, 共 7 頁 (b) Number 47.2417872 Units kg m^2 (c) Number 15.7472624 Units kg m^2 14. *Chapter 10, Problem 43 The uniform solid block in Fig. 10-35 has mass 27.6 kg and edge lengths a = 0.891 m, b = 1.82 m, and c = 0.0735 m. Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces. Fig. 10-35 Problem 43. Number 37.7777852 Units kg m^2 15. *Chapter 10, Problem 41 In the figure, two particles, each with mass m = 0.86 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 6.0 cm and mass M = 1.2 kg. The combination rotates around the rotation axis with angular speed ω = 0.26 rad/s. Measured about O, what is the combination's kinetic energy? Number 0.0009126 Units J 16. *Chapter 10, Problem 57 A pulley, with a rotational inertia of 8.0 x 10-4 kg m 2 about its axle and a radius of 6.1 cm, is acted on by a force applied tangentially at its rim. The force magnitude varies in time as F = 0.48t + 0.39t 2, with F in newtons and t in seconds. The pulley is initially at rest. At t = 3.6 s what are (a) its angular acceleration and (b) its angular speed?

第 6 頁, 共 7 頁 (a) Number 517.158 Units rad/s^2 (b) Number 699.6456 Units rad/s 17. *Chapter 10, Problem 71 In Fig.10-47, two 7.60 kg blocks are connected by a massless string over a pulley of radius 2.30 cm and rotational inertia 7.40 10-4 kg m 2. The string does not slip on the pulley; it is not known whether there is friction between the table and the sliding block; the pulley's axis is frictionless. When this system is released from rest, the pulley turns through 0.800 rad in 172 ms and the acceleration of the blocks is constant. What are (a) the magnitude of the pulley's angular acceleration, (b) the magnitude of either block's acceleration, (c) string tension T 1, and (d) string tension T 2? Assume free-fall acceleration to be equal to 9.81 m/s 2. Fig. 10-47 Problem 71. (a) Number 54.083288263926 Units rad/s^2 (b) Number 1.243915630070 Units m/s^2 (c) Number 65.102241211466 Units N (d) Number 63.362170197757 Units N 18. *Chapter 10, Problem 66 A uniform spherical shell of mass M = 18.0 kg and radius R = 0.500 m can rotate about a vertical axis on frictionless bearings (Fig. 10-44). A massless cord passes around the equator of the shell, over a pulley of rotational inertia I = 0.170 kg m 2 and radius r = 0.120 m, and is attached to a small object of mass m = 2.80 kg. There is no friction on the pulley's axle; the cord does not slip on the pulley. What is the speed of the object when it has fallen a distance 1.44 m after being released from rest? Use energy considerations. Fig. 10-44 Problem 66. Number 1.723463663491 Units m/s

第 7 頁, 共 7 頁 19. *Chapter 10, Problem 67 Figure shows a rigid assembly of a thin hoop (of mass m = 0.11 kg and radius R = 0.12 m) and a thin radial rod (of length L = 2R and also of mass m = 0.11 kg). The assembly is upright, but we nudge it so that it rotates around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in the nudge is negligible, what is the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation? Number 10.982503567738 Units rad/s 20. *Chapter 10, Problem 81 The thin uniform rod in Fig. 10-50 has length 8.0 m and can pivot about a horizontal, frictionless pin through one end. It is released from rest at angle θ = 60 above the horizontal. Use the principle of conservation of energy to determine the angular speed of the rod as it passes through the horizontal position. Assume free-fall acceleration to be equal to 9.83 m/s 2. Fig. 10-50 Problem 81. Number 1.786724977354 Units rad/s