Pagpalain ka! (Good luck, in Filipino) Date Chapter 8 - Rotational Dynamics and Equilibrium REVIEW TRUE/FALSE. Write 'T' if the statement is true and 'F' if the statement is false. 1) When a rigid body rotates about a fixed axis all the points in the body have the same linear displacement. 2) When a rigid body rotates about a fixed axis all the points in the body have the same angular speed. 3) Unbalanced torques produce rotational accelerations, and balanced torques produce rotational equilibrium. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 4) If a constant net torque is applied to an object, that object will A) having an increasing moment of inertia. B) rotate with constant angular velocity. C) rotate with constant linear velocity. D) rotate with constant angular acceleration. E) having a decreasing moment of inertia. 5) What condition or conditions is/are necessary for rotational equilibrium? A) ΣF x = 0 B) ΣF y = 0 C) ΣF x = 0, ΣF y = 0 D) Στ = 0 E) ΣF x = 0, ΣF y = 0, Στ = 0 6) A solid cylinder and a hollow cylinder have the same mass and the same radius. Which statement is true concerning their moment of inertia about an axis through the exact center of the flat surfaces? A) The solid cylinder has the greater moment of inertia. B) The hollow cylinder has the greater moment of inertia. C) Both cylinders have the same moment of inertia. D) The moment of inertia cannot be determined since it depends on the amount of material removed from the inside of the hollow cylinder. 7) What condition or conditions is/are necessary for static equilibrium? A) ΣF x = 0, ΣF y = 0, Στ = 0 B) ΣF y = 0 C) Στ = 0 D) ΣF x = 0, ΣF y = 0 E) ΣF x = 0 8) A ball, solid cylinder, and a hollow pipe all have equal masses and radii. If the three are released simultaneously at the top of an inclined plane, which will reach the bottom first? A) ball B) cylinder C) pipe D) they all reach bottom in the same time 1
9) An ice skater performs a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his angular momentum about the axis of rotation? A) It decreases. B) It does not change. C) It changes, but it is impossible to tell which way. D) It increases. 10) An ice skater performs a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his moment of inertia about the axis of rotation? A) It increases. B) It does not change. C) It changes, but it is impossible to tell which way. D) It decreases. 11) An ice skater performs a pirouette (a fast spin) by pulling in his outstretched arms close to his body. What happens to his rotational kinetic energy about the axis of rotation? A) It increases. B) It decreases. C) It does not change. D) It changes, but it is impossible to tell which way. 12) A boy and a girl are riding on a merry-go-round that is turning. The boy is twice as far as the girl from the merry-go-round's center. If the boy and girl are of equal mass, which statement is true about the boy's moment of inertia with respect to the axis of rotation? A) His moment of inertia is 4 times the girl's. B) The boy has a greater moment of inertia, but it is impossible to say exactly how much more. C) The moment of inertia is the same for both. D) His moment of inertia is half the girl's. E) His moment of inertia is twice the girl's. 13) Two equal forces are applied to a door at the doorknob. The first force is applied perpendicular to the door; the second force is applied at 30 to the plane of the door. Which force exerts the greater torque? A) the first applied perpendicular to the door B) both exert zero torques C) the second applied at an angle D) both exert equal non-zero torques E) additional information is needed 14) Consider a rigid body that is rotating. Which of the following is an accurate statement? A) Its center of rotation must be moving with a constant velocity. B) Its center of rotation must be at rest, i.e., not moving. C) All points on the body are moving with the same angular velocity. D) All points on the body are moving with the same linear velocity. E) Its center of rotation is its center of gravity. 2
FIGURE 8-1 15) Five forces act on a massless rod free to pivot at point P, as shown in Fig. 8-1. Which force is producing a counter-clockwise torque about point P? A) A B) B C) C D) D E) E SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 16) If the net force on an object is zero N, does the net torque on the object have to be zero Nm? 17) Is it easier to swing a bat holding the handle at the end, or "choked up"? Why? 18) The moment of inertia of a solid sphere about any diameter is 2/5 MR2. What is the moment of inertia about an axis that is tangent to the surface? PROBLEMS. Answer each question by showing ALL WORK and circle or box your answer to find easier. 19) A 30.0-kg child sits on one end of a long uniform beam with a mass 20.0 kg and a 40.0-kg child sits on the other end. The beam balances when a fulcrum is placed below the beam a distance 1.10 m from the 30.0-kg child. How long is the beam? 3
20) A girl weighing 450. N sits on one end of a seesaw that is 3.0 m long and is pivoted 1.3 m from the girl. If the seesaw is just balanced when a boy sits at the opposite end, what is his weight? Neglect the weight of the seesaw. 21) Consider a bicycle wheel to be a ring of radius 30. cm and mass 1.5 kg. Neglect the mass of the axle and sprocket. If a force of 20. N is applied tangentially to a sprocket of radius 4.0 cm for 4.0 s, what linear speed does the wheel achieve, assuming it rolls without slipping? 22) A ballerina spins initially at 1.5 revolutions/second when her arms are extended. She then draws in her arms to her body and her moment of inertia becomes 0.88 kg-m2 and her angular speed increases to 4.0 rev/s. Determine her initial moment of inertia. 23) An object's angular momentum changes by 10 kg-m2/s in 2.0 s. What magnitude average torque acted on this object? 4
24) An 8.0 kg-m 2 wheel with 155. J of rotational kinetic energy requires what torque to bring it to rest in 4.0 s? 25) A ball with diameter 10. cm rolls without slipping on a horizontal table top. The moment of inertia of the ball is 2.2 10-3 kg-m2 and its translational speed is 0.45 m/s. (a) What is its angular speed about its center of mass? (b) What is its rotational kinetic energy? (c) What is its angular momentum? 26) A 82.0 kg painter stands on a long horizontal board 1.55 m from one end. The 15.5 kg board is 5.50 m long. The board is supported at each end. (a) What is the total force provided by both supports? (b) With what force does the support, closest to the painter, push upward? 27) A 1.8 kg solid disk pulley of radius 0.11 m rotates about an axis through its center. (a) What is its moment of inertia? (b) Starting from rest, a torque of 0.22 m-n will produce what angular acceleration? 5
FIGURE 8-4 28) A uniform solid cylinder (mass 100. kg and radius 50.0 cm) is mounted so it is free to rotate about fixed horizontal axis that passes through the centers of its circular ends. A 10.0 kg block is hung from a massless cord wrapped around the cylinder's circumference. When the block is released, the cord unwinds and the block accelerates downward, as shown in Fig. 8-4. What is the block's acceleration? FIGURE 8-7 29) A uniform rod has a length of 2.0 m. It is hinged to a wall (at the left end), and held in a horizontal position by a vertical massless string (at the right end), as shown in Fig. 8-7. What is the angular acceleration of the rod at the moment the string is released? 6
Answer Key Testname: CH8 ROT DYNAMICS REVIEW 1) FALSE 2) TRUE 3) TRUE 4) D 5) D 6) B 7) A 8) A 9) B 10) D 11) A 12) A 13) A 14) C 15) C 16) No. For example, the object might be subjected to two equal and opposite forces that are not along the same straight line. This would produce a torque, but the net force would be zero N. 17) "Choked up", because the moment of inertia is less about the axis of rotation (bat center of mass moved toward axis). 18) 2/5 MR2 + MR2 = 7/5 MR2 19) 1.98 m 20) 344. Newtons 21) 7.11 m/s 22) 2.3 kg m2 23) 5 N-m 24) -1.0 N-m 25) (a) 9.0 rad/s (b) 0.089 J (c) 0.020 J s 26) (a) 956. N (b) 653. N 27) (a) 1.1 10-2 kg m2 (b) 20. rad/s2 28) 1.63 m/s2 29) 7.4 rad/s2 7