1、Chapter 8 rotational motion第 1 页 共 7 页Kinematics1. What is the angular displacement of each of the following hands of a clock in 1 h?State your answer in three significant digits.(a). the second hand .(b). the minute hand .(c). the hour hand.2. A rotating toy above a babys crib makes one complete co
2、unterclockwise rotation in 1 min.A.What is its angular displacement in 3 min ? B.What is the toys angular velocity in rad/min ?C.If the boy is turned off, does it have positive or negative angular acceleration ? Explain .3.If a truck has a linear acceleration of 1.85 m/s2 and the wheels have an angu
3、lar acceleration of 5.23 rad/s2, what is the diameter of the trucks wheels?4. The truck in the previous problem is towing a trailer with wheels that have a diameter of 48 cm.a. How does the linear acceleration of the trailer compare with that of the truck?b. How do the angular accelerations of the w
4、heels of the trailer and the wheels of the truck compare?5. You want to replace the tires on your car with tires that have a larger diameter. After youchange the tires, for trips at the same speed and over the same distance, how will theangular velocity and number of revolutions change?6.If the radi
5、us of a CD is 6.0 cm and the angular velocity is 5.0 rad/s . What is the linear displacement of a point on the edge is 2.0 s ?(A). 0.30 m (B). 0.60 m (C). 3.8 m (D). 60 mTorque1. A door (seen from above in the figures below) has hinges on the left hand side. Which force produces the largest torque?
6、The magnitudes of all forces are equal.Chapter 8 rotational motion第 2 页 共 7 页2.A rod on a horizontal tabletop is pivoted at one end and is free to rotate without friction about a vertical axis, as shown. A force F is applied at the other end, at an angle to the rod. If F were to be applied perpendic
7、ular to the rod, at what distance from the axis should it be applied in order to produce the same torque?(A) L sin (B) L cos (C) L (D) L tan 3.In which of the following diagrams is the torque about point O equal in magnitude to the torque about point X in the diagram? (All forces lie in the plane of
8、 the paper.)4. A 5-meter uniform plank of mass 100 kilograms rests on the top of a building with 2 meters extended over the edge as shown. How far can a 50-kilogram person venture past the edge of the building on the plank before the plank just begins to tip?(A) 0.5 m (B) 1 m (C) 1.5 m ( D) 2 m5.A u
9、niform meterstick of mass 0.20 kg is pivoted at the 40 cm mark. Where should one hang a mass of 0.50 kg to balance the stick? (A) 16 cm (B) 36 cm (C) 44 cm (D) 46 cm 6.To weigh a fish, a person hangs a tackle box of mass 3.5 kilograms and a cooler of mass 5 kilograms from the ends of a uniform rigid
10、 pole that is suspended by a rope attached to its center. The system balances when the fish hangs at a point 1/4 of the rods length from the tackle box. What is the mass of the fish?(A) 1.5 kg (B) 2 kg (C) 3 kg (D) 6 kg Chapter 8 rotational motion第 3 页 共 7 页7.Two objects, of masses 6 and 8 kilograms
11、, are hung from the ends of a stick that is 70 cm long and has marks every 10 cm, as shown. If the mass of the stick is negligible, at which of the points indicated should a cord be attached if the stick is to remain horizontal when suspended from the cord?(A) A (B) B (C) C (D) D 8.A square piece of
12、 plywood on a horizontal tabletop is subjected to the two horizontal forces shown. Where should a third force of magnitude 5 newtons be applied to put the piece of plywood into equilibrium?9.A wheel of radius R and negligible mass is mounted on a horizontal frictionless axle so that the wheel is in
13、a vertical plane. Three small objects having masses m, M, and 2M, respectively, are mounted on the rim of the wheel, as shown. If the system is in static equilibrium, what is the value of m in terms of M?(A) M/2 (B) M (C) 3M/2 (D) 5M/2 10.A system of two wheels fixed to each other is free to rotate
14、about a frictionless axis through the common center of the wheels and perpendicular to the page. Four forces are exerted tangentially to the rims of the wheels, as shown. The magnitude of the net torque on the system about the axis is(A) zero (B) 2FR (C) 5FR (D) 14FRRotational Kinematics and Dynamic
15、s1.Two small “weights,” of mass 5.0 kg and 7.0 kg, are mounted 4.0 m apart on a light rod (whose mass can be ignored), as shown in Fig. Calculate the moment of inertia of the system (a) when rotated about an axis halfway between the weights, Fig a, and (b) when rotated about an axis 0.50 m to the le
16、ft of the 5.0-kg mass (Fig)Chapter 8 rotational motion第 4 页 共 7 页2.A 15.0-N force (represented by FT ) is applied to a cord wrapped around a pulley of mass M=4.00kg and radius R=33.0cm Fig. The pulley accelerates uniformly from rest to an angular speed of 30.0 rad/s in 3.00 s. If there is a friction
17、al torque fr=1.10 mN at the axle, determine the moment of inertia of the pulley. The pulley rotates about its center.3.A uniform stick has length L. The moment of inertia about the center of the stick is Io. A particle of mass M is attached to one end of the stick. The moment of inertia of the combi
18、ned system about the center of the stick is(A) (B) (C) (D) 2014I201I2034IML20IL4.A light rigid rod with masses attached to its ends is pivoted about a horizontal axis as shown above. When released from rest in a horizontal orientation, the rod begins to rotate with an angular acceleration of magnitu
19、de(A) (B) (C) (D) gl7l5gl457l5.Two blocks are joined by a light string that passes over the pulley shown above, which has radius R and moment of inertia I about its center. T1 and T2 are the tensions in the string on either side of the pulley and is the angular acceleration of the pulley. Which of t
20、he following equations best describes the pulleys rotational motion during the time the blocks accelerate?(A) m2gR = I (B) T2R = I (C) (T2 - T1)R = I (D) (m2 m1)gR = IEquilibrium ，Center mass and Stability1. A non-uniform plank of wood XY is 2.50 m long and weighs 950 N. Force-meters (spring balance
21、s) A and B are attached to the plank at a distance of 0.40 m from each end, as illustrated in Fig.Chapter 8 rotational motion第 5 页 共 7 页When the plank is horizontal, force-meter A records 570 N.(i) Calculate the reading on force-meter B.reading = N(ii) On Fig , mark a likely position for the center
22、of gravity of the plank.(iii) Determine the distance of the center of gravity from the end X of the plank.distance = . m62. The diagram shows sections of four objects, all of equal mass. The position of the centre of mass of each object has been marked with a cross. Which object is the most stable?3
23、.The diagram shows four models of buses placed on different ramps. How many of these models will fall over ?A 1 B 2 C 3 D 44.The diagram shows four objects standing on a flat surface. The centre of mass of each object is marked M. Which object will fall over?Angular Momentum and its ConservationChap
24、ter 8 rotational motion第 6 页 共 7 页1. A simple clutch consists of two cylindrical plates that can be pressed together to connect two sections of an axle, as needed, in a piece of machinery. The two plates have masses MA=6.0 kg and MB=9.0kg with equal radii R=0.60 m. They are initially separated (Fig)
25、. Plate is accelerated from rest to an angular velocity 1=7.2 rad/sin time t =2.0s. Calculate (a) the angular momentum of MA and (b) the torque required to accelerate from rest to 1 (c) Next, plate MB initially at rest but free to rotate without friction, is placed in firm contact with freely rotati
26、ng plate MA , and the two plates then both rotate at a constant angular velocity 2, which is considerably less than 1.Why does this happen, and what is 2 ?The rotational inertia of the cylinder about its axis is 2MR22.An ice skater is spinning about a vertical axis with arms fully extended. If the a
27、rms are pulled in closer to the body, in which of the following ways are the angular momentum and kinetic energy of the skater affected?Angular Momentum Kinetic Energy(A) Increases Increases(B) Increases Remains Constant(C) Remains Constant Increases(D) Remains Constant Remains Constant3.A particle
28、of mass m moves with a constant speed v along the dashed line y = a. When the x-coordinate of the particle is xo, the magnitude of the angular momentum of the particle with respect to the origin of the system is(A) zero (B) mva (C) mvxo (D) 20mvxa4.The rigid body shown in the diagram above consists
29、of a vertical support post and two horizontal crossbars with spheres attached. The masses of the spheres and the lengths of the crossbars are indicated in the diagram. The body rotates about a vertical axis along the support post with constant angular speed . If the masses of the support post and th
30、e crossbars are negligible, what is the ratio of the angular momentum of the two upper spheres to that of the two lower spheres?(A) 2/1 (B) 1/2 (C) 1/4 (D) 1/8Chapter 8 rotational motion第 7 页 共 7 页Top View5.Multiple Correct. A disk sliding on a horizontal surface that has negligible friction collide
31、s with a rod that is free to move and rotate on the surface, as shown in the top view above. Which of the following quantities must be the same for the disk-rod system before and after the collision? Select two answers.I. Linear momentum II. Angular momentum III. Kinetic energy(A) Linear Momentum (B) Angular Momentum (C) Kinetic Energy (D) Mechanical Energy
