Chapter 8 Rotational Motion and Equilibrium Name 1. Give explanation of torque in own words after doing balance-the-torques lab as an inquiry introduction 1. The distance between a turning axis and the point of contact of a perpendicular force is called the fulcrum. a. T b. F False: it is the moment arm 2. To turn a stubborn screw, it is best to use a screwdriver that has a a. long handle b. wide handle c. yellow handle d. red handle B Wide handle with same force gives greater torque 2. Locate center of mass of an object, showing force acting via free-body diagram 3. The center of mass of an object is always located at the object s geometric center. a. T b. F False it depends on where the weight is distributed. 4. The long heavy tail of a spider monkey enables the monkey to easily vary its. a. weight b. momentum c. center of gravity d. none of these C by moving the tail towards and away from body or up or down. 5. When a wrench is slid spinning over a frictionless tabletop, its center of gravity follows a. a wobbly path with irregular speed. b. a regular straight-line path. c. a straight-line path with irregular speed B See diagram in the book. 6. The center of gravity of an object can be located by. a. looking at the intersection of lines drawn from suspension points. b. balancing it above your finger. c. drawing lines down from suspension points. d. all of the above will work D See section 8.3 in text book.
7. An object thrown into the air rotates about its. a. midpoint. b. center of gravity. c. geometric center. d. edge. e. none B see text 8. A ball resting on the floor is in what kind of equilibrium? a. Neutral b. Stable c. Unstable B stable. See the book p 213. 3. Determine whether an object will tip over based on locations of axis of rotation and center of mass 10. An unaided object will topple over when its center of gravity extends beyond its support base. a. T b. F True: see lab and book 11. When you carry a heavy load with one arm like a bucket full of water, why do you tend to hold your free arm away from your body? a. to change the center of gravity of your body and the load b. to change the mass of your body c. to look way sweet d. to change how much weight you and your load has A see lab 12. If an object is in stable equilibrium, any displacement will. a. decrease its mass. b. lower its center of gravity. c. raise its center of gravity. d. increase its mass. e. neither raise nor lower its center of gravity. c See book.
4. Calculate torque, include situations where force is not perpendicular to radius 15. You exert 300 Newtons of force on your bike pedal at an angle of 60 degrees. The length from the axis of rotation on the wheel to the pedal is 20 centimeters. What torque do you apply to the bike wheel? a. 51.96 N m b. 60 N m c. 5196.2 N m θ d. 6000 N m A- rf(sinө) Calculate missing torque needed to establish equilibrium 17. Two people sit on a balanced see-totter. When one person leans toward the center of the teetersaw, that person s end of the see-totter will a. fall b. rise c. stay at the same level B moment arm decreases 18. A 400-gram mass is attached to the 20-cm position on a meter stick that is suspended from a hanging string at the 50-cm position. If a mass of 600-grams is attached to the second side of the suspended stick, at what METER STICK POSITION should you attach the 600-gram mass? a. 90 cm b. 80 cm c. 70 cm d. 50 cm e. 20 cm C-Use torques.
20. Your physics teacher has a mass of 80-kg while holding his calculator, 3-ring binder, pens, and grade book. He is forced to walk the plank by his unruly classes the plank is 4.0-meters long and sits atop the lab bench. The 4.0-meter long plank has 0.5-meters extending past the bench and 3.5- meters still above the bench. While standing at the very end of the plank your teacher just balances. What is the mass of the plank? a. 24.7 kg b. 11.4 kg c. 26.7 kg d. 20 kg e. 10 kg C-26.7kg or 261N 5. Determine arc length, angular velocity, and angular acceleration. 22. The rotational velocity of a 45 rev/min record in radians/sec is approximately: a. 45 rad/sec b. 283 rad/sec c. 0.75 rad/sec d. 4.7 rad/sec e. 15.7 rad/sec D -4.7rad/sec 24. The armature of a motor is accelerated uniformly from rest to a rotational velocity of 1800 rev/min in 10.0 seconds time. The rotational acceleration of the motor is: a. 180 rad/sec 2 b. 90 rad/sec 2 c. 37.7 rad/sec 2 d. 18.8 rad/sec 2 D-18.8rad/s 2
6. Demonstrate conceptual knowledge of moment of inertia and how it is affected by changing mass distribution 27. When a gymnast moves from an extended position to a tucked position, she. a. decreases her moment of inertia b. increases her moment of inertia c. neither a or b A-r decreases m stays the same. 28. A short pendulum has a larger moment of inertia than a long pendulum of the same mass. a. T b. F False-a smaller one m is the same r is less. 29. Dancers may change their moment of inertia while going through a break-dance routine. a. T b. F True: change r for arms and legs. 1) The condition for rolling without slipping is that the center of mass speed is 2 A) vcm = rω B) vcm = 2rω rω C) vcm = 2 D) vcm = rω 2 E) = r ω vcm Answer: D 3) A 50. cm diameter wheel is rotating initially at 2.0 revolutions per second. It slows down uniformly and comes to rest in 15.seconds. (a) What was its angular acceleration? Answer: (a) -0.13 rev/s 2 ; -0.84 rad/s 2 Diff: 3
4) A wheel of diameter 0.70m rolls without slipping. A point at the top of the wheel moves with a tangential speed 2.0 m/s. (b) What is the angular speed of the wheel? Answer: (b) 5.8 rad/s Diff:3 5) A pencil balanced on its tip such that it does not move A) is in unstable equilibrium. B) has a net torque acting on it. C) has a net vertical force. D) has a zero moment of inertia. Answer: A 6) A wheel slows down uniformly and comes to rest in 15. seconds. It is rotating initially at 2.0 revolutions per second and has a diameter of 50.cm. (b) What was the tangential acceleration? Answer: (b) -0.21 m/s 2 Diff: 3 7) A cylinder, of radius 8.0 cm, rolls 20.cm in 5.0s. (a) Through what angular displacement does the cylinder move in this time? (b) What is the angular speed? Answer: (a) 2.5 radians (143 ) (b) 0.50 rad/sec 8) A bicycle is moving 4.0 m/s. What is the angular speed of a wheel if its radius is 30.cm? A) 4.8 rad/s B) 7.6 rad/s C) 0.36 rad/s D) 1.2 rad/s E) 13. rad/s Answer: E Diff:2
1) What condition or conditions is/are necessary for rotational equilibrium? A) F = 0 y x B) F = 0, F = 0 C) τ = 0 D) F = 0 x x y E) F = 0, F = 0, τ = 0 y Answer: C 2) A girl weighing 450. N sits on one end of a seesaw that is 3.0 m long and is pivoted 1.3m from the child. If the seesaw is just balanced when a boy sits at the opposite end, what is his weight? Neglect the weight of the seesaw. Answer: 344. newtons Diff:2 5) Five forces act on a massless rod free to pivot at point P. Which force is producing a counter-clockwise (out of the paper) torque about point P? A) A B) B C) C D) D E) E Answer: C
9) A boy and a girl are balanced on a massless seesaw. The boy has a mass of 60 kg and the girl's mass is 50 kg. If the boy sits 1.5m from the pivot point on one side of the seesaw, where must the girl sit on the other side for equilibrium? A) 3.0 m B) 1.3m C) 2.5 m D) 1.8m Answer: D 6) A uniform rod has a weight of 40.N and a length of 1.0m. 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). What is the magnitude of the torque exerted by the string about a horizontal axis which passes through the hinge and is perpendicular to the rod? A) 40 N-m B) 10 N-m C) 5.0 N-m D) 20 N-m E) 30 N-m Answer: D 8) What condition or conditions is/ are necessary for static equilibrium? A) F = 0 y x B) F = 0, F = 0 C) τ = 0 D) F = 0 x x y E) F = 0, F = 0, τ = 0 y Answer: E Diff:2
10) A heavy boy and a lightweight girl are balanced on a massless seesaw. If they both move forward so that they are one-half their original distance from the pivot point, what will happen to the seesaw? A) It is impossible to say without knowing the masses and the distances. B) The side the boy is sitting on will lilt downward. C) Nothing, the seesaw will still be balanced. D) The side the girl is silting on will lilt downward. Answer: C 11) "Lever Arm" can have which of the following units? (a) Joules (b) N.m2 (c) kg.m 2 /s (d) kg.m / s2 (e) meters Answer: (e) meters 13) A force is applied to the end of a 2.0m long uniform board weighing 50.N, in order to keep it horizontal, while it pushes against a wall at the left. If the angle the force makes with the board is 30 in the direction shown, what is the applied force F? A) 58.N B) 50.N C) 29.N D) 90.N E) 32.N Answer: B 8.3 Rotational Dynamics 3) Torque has which of the following units? (a) joules (b) N m (c) kg m 2 /s (d) kg m 2 /s 2 (e) kg m 2 Answer: (b) N m Diff:1
5) Is it easier (less torque) to swing a bat holding the handle at the end, or "choked up"? Why? Answer: "Choked up", because the moment of inertia is less about the axis of rotation (bat center of mass moved toward axis). 6) Consider a solid object which is subjected to a net torque. That object will experience which of the following? A) a linear acceleration and an angular acceleration B) an angular acceleration C) a constant angular velocity D) a changing moment of inertia Answer: B 14) 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 does not change. B) It decreases. C) It increases. D) It changes, but it is impossible to tell which way. Answer: B Diff:2 16) 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 hollow cylinder has the greater moment of inertia. B) The solid 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.. Answer: A 20) Consider two uniform solid spheres where both have the same diameter, but one has twice the mass of the other. The ratio of the larger moment of inertia to that of the smaller moment of inertia is A) 2. B) 10. C) 4. D) 8. E) 6. Answer: A Diff:2
23) Moment of Inertia has which of the following units? (a) joules (b) N.m (c) kg.m 2 /s (d) kg.m 2 /s 2 (e) kg.m 2 Answer: (e) kg-m 2 Difficult 4) An 82.0 kg painter stands on a long horizontal board 1.55m 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? Answer: (a) 956. N (b) 653. N Diff: 3 4) A 2.50 kg is at (r1.00, 3.00) meters. What is the moment of inertia: (a) about the x-axis? (b) about the y-axis? (c) about the line defined by x= 6.00 m? Answer: (a) 2.50 kg-m 2 (b) 22.5 kg-m 2 (c) 62.5 kg-m 2 Diff: 3