Unit 4 Practice Test: Rotational Motion Multiple Guess Identify the letter of the choice that best completes the statement or answers the question. 1. How would an angle in radians be converted to an angle in degrees? a. The angle in radians would be multiplied by 180 /π. b. The angle in radians would be multiplied by 360 /π. c. The angle in radians would be multiplied by 180 /2π. d. The angle in radians would be multiplied by 2π/360. 2. How would you convert an angle in degrees to an angle in radians? a. multiply the angle measured in degrees by 2π/180 b. multiply the angle measured in degrees by 2π/360 c. multiply the angle measured in degrees by π/360 d. multiply the angle measured in degrees by 2πr 3. A child sits on a carousel at a distance of 3.5 m from the center and rotates through an arc length of 6.5 m. What is the angular displacement of the child? a. 1.9 rad c. 3.0 rad b. 0.93 rad d. 5.0 rad 4. A bucket on the circumference of a water wheel travels an arc length of 18 m. If the radius of the wheel is 4.1 m, what is the angular displacement of the bucket? a. 1.0 rad c. 3.7 rad b. 4.4 rad d. 2.3 rad 5. What is the approximate angular speed of a wheel rotating at the rate of 5.0 rev/s? a. 3.2 rad/s c. 16 rad/s b. 1.6 rad/s d. 31 rad/s 6. A potter's wheel moves from rest to an angular speed of 0.54 rad/s in 30.0 s. What is the angular acceleration of the wheel? a. 16 rad/s 2 c. 0.018 rad/s 2 b. 1.3 rad/s 2 d. 0.042 rad/s 2 7. A record player is turned on and reaches an angular velocity of 4.7 rad/s in 1.37 s. What is the average angular acceleration of the record? a. 3.4 rad/s 2 c. 6.4 rad/s 2 b. 4.3 rad/s 2 d. 0.29 rad/s 2 8. A bicycle wheel rotates with a constant angular acceleration of 3.0 rad/s 2. If the initial angular speed of the wheel is 1.5 rad/s, what is the angular displacement of the wheel after 4.0 s? a. 6.0 rad c. 3.0 10 1 rad b. 24 rad d. 36 rad 9. A ball rolls downhill with an angular speed of 2.5 rad/s and has a constant angular acceleration of 2.0 rad/s 2. If the ball takes 11.5 s to reach the bottom of the hill, what is the final angular speed of the ball? a. 13 rad c. 33 rad/s b. 31 rad/s d. 25.5 rad/s 10. The end of the cord on a weed cutter is 0.15 m in length. If the motor rotates at the rate of 126 rad/s, what is the tangential speed of the cord? a. 628 m/s c. 19 m/s b. 25 m/s d. 63 m/s 11. A cylinder with a diameter of 0.150 m rotates in a lathe at a constant angular speed of 35.6 rad/s. What is the tangential speed of the surface of the cylinder? a. 2.67 m/s c. 2.37 10 2 m/s b. 5.34 m/s d. 4.75 10 2 m/s
12. A flywheel with a radius of 0.30 m starts from rest and accelerates with a constant angular acceleration of 0.50 rad/s 2. What is the tangential acceleration of the flywheel? a. 0.63 m/s 2 c. 0.65 m/s 2 b. 0.15 m/s 2 d. 1.30 m/s 2 13. A contestant in a game show spins a stationary wheel with a radius of 0.50 m so that it has a constant angular acceleration of 0.40 rad/s 2. What is the tangential acceleration of a point on the edge of the wheel? a. 0.20 m/s 2 c. 1.3 m/s 2 b. 0.60 m/s 2 d. 0.73 m/s 2 14. A point on the rim of a rotating wheel with a 0.37 m radius has a centripetal acceleration of 19.0 m/s 2. What is the angular speed of the wheel? a. 0.89 m/s c. 3.2 rad/s b. 1.6 rad/s d. 7.2 rad/s 15. A roller coaster loaded with passengers has a mass of 2.0 10 3 kg; the radius of curvature of the track at the lowest point of the track is 24 m. If the vehicle has a tangential speed of 18 m/s at this point, what force is exerted on the vehicle by the track? a. 2.3 10 4 N c. 3.0 10 4 N b. 4.7 10 4 N d. 2.7 10 4 N 16. What is the gravitational force between two trucks, each with a mass of 2.0 10 4 kg, that are 2.0 m apart? (G = 6.673 10 11 N m 2 /kg 2 ) a. 5.7 10 2 N c. 6.7 10 3 N b. 1.3 10 2 N d. 1.2 10 7 N 17. The gravitational force between two masses is 36 N. What is the gravitational force if the distance between them is tripled? (G = 6.673 10 11 N m 2 /kg 2 ) a. 4.0 N c. 18 N b. 9.0 N d. 27 N 18. Which of the following quantities measures the ability of a force to rotate or accelerate an object around an axis? a. axis of rotation c. moment arm b. lever arm d. torque 19. Which of the following statements is correct? a. The farther the force is from the axis of rotation, the more torque is produced. b. The closer the force is to the axis of rotation, the more torque is produced. c. The closer the force is to the axis of rotation, the easier it is to rotate the object. d. The farther the force is from the axis of rotation, the less torque is produced. 20. A heavy bank-vault door is opened by the application of a force of 3.0 10 2 N directed perpendicular to the plane of the door at a distance of 0.80 m from the hinges. What is the torque? a. 120 N m c. 300 N m b. 240 N m d. 360 N m 21. Suppose a doorknob is placed at the center of a door. Compared with a door whose knob is located at the edge, what amount of force must be applied to this door to produce the torque exerted on the other door? a. one-half as much c. one-fourth as much b. two times as much d. four times as much
22. At which point in the figure above is the approximate center of mass? a. A c. C b. B d. D 23. At which point on the hammer above is the approximate center of mass? a. A c. C b. B d. D 24. Which of the following statements is correct? a. The farther the center of mass of an object is from the axis of rotation, the less difficult it is to rotate the object. b. The farther the center of mass of an object is from the axis of rotation, the smaller the object s moment of inertia is. c. The farther the center of mass of an object is from the axis of rotation, the greater the object s moment of inertia is. d. The farther the center of mass of an object is from the axis of rotation, the greater the object s moment of inertia is, but the less difficult it is to rotate the object. 25. The dependence of equilibrium on the absence of net torque is a. the first condition of equilibrium. c. rotational equilibrium. b. the second condition of equilibrium. d. translational equilibrium. 26. A child with a weight of 4.50 10 2 N sits on a seesaw 0.60 m from the axis of rotation. How far from the axis of rotation on the other side should a child with a weight of 6.00 10 2 N sit so the seesaw will remain balanced? a. 0.30 m c. 0.45 m b. 0.40 m d. 0.50 m 27. According to Newton s second law, the angular acceleration experienced by an object is directly proportional to which of the following? a. the object s moment of inertia c. the size of the object b. the net applied torque d. the mass of the object 28. Which of the following statements is correct? a. With a net positive torque, the angular acceleration of an object is clockwise. b. With a net positive torque, the angular acceleration of an object is counterclockwise. c. With a net negative torque, the angular acceleration of an object is counterclockwise. d. The net force of an object is not related to the translational acceleration given to the object.
29. Which of the following represents Newton s second law for rotating objects? a. net torque = moment of inertia angular acceleration b. net torque = moment of inertia angular acceleration c. force = mass acceleration d. force = mass acceleration 30. A figure skater with arms drawn in spins on the ice at a rate of 5.0 rad/s and has a moment of inertia of 1.875 kg m 2. What is the angular momentum of the skater? a. 2.5 kg m 2 /s c. 9.4 kg m 2 /s b. 3.8 kg m 2 /s d. 12 kg m 2 /s 31. The moment of inertia of a cylinder is 0.016 kg m 2. If the angular speed is 15.7 rad/s, what is the angular momentum of the cylinder? a. 0.25 kg m 2 /s c. 19.2 kg m 2 /s b. 12.1 kg m 2 /s d. 28.6 kg m 2 /s 32. A bowling ball has a mass of 7.0 kg, a moment of inertia of 2.8 10 2 kg m 2, and a radius of 0.10 m. If it rolls down the lane without slipping at a linear speed of 4.0 m/s, what is its total kinetic energy? a. 45 J c. 11 J b. 32 J d. 78 J Short Answer 33. Is there an outward force in circular motion? 34. A ball is whirled in a horizontal circular path on the end of a string. Predict the path of the ball when the string breaks, and explain your answer. 35. A parent holds a child by the arms and spins around in a circle at a constant speed. If the parent spins fast enough, will the child's feet leave the ground? Explain your answer. 36. What is the main difference between mass and moment of inertia? 37. Define the second condition of equilibrium. 38. How can an object be in both rotational and translational equilibrium? 39. Describe Newton s second law of rotation. 40. Explain how the operation of a simple machine alters the applied force and the distance moved. Problem #41 on back
Problem 41. A 4.0 m board with a mass of 19 kg is pivoted at its center of gravity. A helium balloon attached 0.23 m from the left end of the board produces an upward force of 7.0 N. A 3.5 kg book is placed 0.73 m from the left end of the board, and another book of 1.3 kg is placed 0.75 m from the right end of the board. Find the torque on the board and the direction of rotation.
Unit 4 Practice Test: Rotational Motion Answer Section MULTIPLE GUESS SHORT ANSWER PROBLEM 1. A 17. A 2. B 18. D 3. A 19. A 4. B 20. B 5. D 21. B 6. C 22. A 7. A 23. D 8. C 24. C 9. D 25. B 10. C 26. C 11. B 27. B 12. B 28. B 13. A 29. A 14. D 30. C 15. D 31. A 16. C 32. D 33. No, there is only an inward force causing a deviation from a straight-line path. 34. Inertia causes the ball to move in a straight path tangent to the circle. 35. As the angular velocity increases, the parent s arms must exert a larger and larger force, F, because the horizontal component of this force, F h, is the centripetal force and this force F c = mrω 2. However, if F increases so does its vertical component. When F is large enough so that its vertical component is equal to the weight of the child, the child s feet leave the ground. 36. Mass resists changes in translational motion, and moment of inertia resists changes in rotational motion. 37. The second condition of equilibrium is the dependence of equilibrium on the absence of net torque. 38. There must be zero net force and zero net torque. 39. Net torque is equal to an object s moment of inertia multiplied by its angular acceleration. 40. A machine can increase or decrease the force acting on an object at the expense or gain of the distance moved. 41. 15 N m counterclockwise