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# jkkl BIO 305

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This 16 page Class Notes was uploaded by Haley Notetaker on Friday August 12, 2016. The Class Notes belongs to BIO 305 at New Mexico State University taught by Champa S. Gopalan in Fall 2016. Since its upload, it has received 11 views. For similar materials see Principles of Genetics in Biology at New Mexico State University.

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Date Created: 08/12/16

Chapter 7, Rotational Motion and the Law of Gravity C HAPTER 7 7.1 Angular Speed and Angular Acceleration 1. 2 600 rev/min is equivalent to which of the following? a. 2600 rad/s b. 43.3 rad/s c. 273 rad/s d. 60 rad/s 2. A grindstonespinning at the rate of 8.3 rev/s has what approximate angular speed? a. 3.2 rad/s b. 26 rad/s c. 52 rad/s d. 81 rad/s 3. A 0.12-m-radius grinding wheeltakes 5.5 s to speedup from 2.0 rad/s to 11.0 rad/s. What is the wheel’s average angular acceleration? 2 a. 9.6 rad/2 b. 4.8 rad/s c. 1.6 rad/s d. 0.33 rad/s 4. What is the angular speed about the rotational axis of the Earth for a person standing onthe surface? −5 a. 7.3 × 1−5rad/s b. 3.6 × 10 rad/s c. 6.28 × 10 rad/s d. 3.14 × 10 rad/s 5. A spool of thread has an average radius of 1.00 cm. If the spool contains 62.8 m of thread, how many turns of thread are on the spool? a. 100 b. 1 000 c. 3 140 d. 62 800 87 Chapter 7, Rotational Motion and the Law of Gravity 6. A ceiling fan is turned onand reaches an angular speed of 120 rev/minin 20 s. It is then turned off and coasts to a stop in an additional 40 s. The ratio of the average angular acceleration for the first 20 s to that for the last 40 s is which of thefollowing? a. 2 b. 0.5 c. –0.5 d. –2 7.2 Rotational Motion Under Constant Angular Acceleration 7. A 0.30-m-radius automobile tire rotates how manyrad after starting from rest and accelerating at a constant 2.0 rad/s over a 5.0-s interval? a. 12.5 rad b. 25 rad c. 2.0 rad d. 0.50 rad 2 8. A fan blade, initially at rest, rotates with a constant acceleration of 0.025 rad/s . What is its angular speed at the instant it goes through an angular displacement of 4.2 rad? a. 0.025 rad/s b. 0.11 rad/s c. 0.46 rad/s d. 1.2 rad/s 9. A fan blade, initially at rest, rotates with a constant acceleration of 0.025 rad/s . What is the time interval required for it to reach a 4.2-rad displacement after starting from rest? a. 1.8 s b. 2.0 s c. 16 s d. 18 s 10. A ceiling fan is turned on and reaches an angular speed of 120 rev/min in 20 s. It is then turned off and coasts to a stop in 40 s. In the one minute of rotation, through how manyrevolutions did the fan turn? a. 20 b. 60 c. 0 d. 600 88 Chapter 7, Rotational Motion and the Law of Gravity 11. Starting from rest, a wheel undergoes constant angular acceleration for a period of timeT. At what time after the start of rotation does the wheel reach an angular speed equal to its average angular speed for this interval? a. 0.25 T b. 0.50 T c. 0.67 T d. 0.71 T 12. Starting from rest, a wheel undergoes constant angular acceleration for a period of timeT. At which of the following times does the average angular acceleration equal the instantaneous angular acceleration? a. 0.50 T b. 0.67 T c. 0.71 T d. all of the above 13. A Ferris wheel starts at rest and builds up to a final angular speed of 0.70 rad/s while rotating through an angular displacement of 4.9 rad. What is its average angular acceleration? 2 a. 0.10 rad/s 2 b. 0.05 rad/s c. 1.8 rad/s2 d. 0.60 rad/s 2 14. A Ferris wheel, rotating initiallyat an angular speed of 0.50 rad/s, accelerates over a 7.0-s interval at a rate of 0.040 rad/s . What is its angular speed after this 7-s interval? a. 0.20 rad/s b. 0.30 rad/s c. 0.46 rad/s d. 0.78 rad/s 15. A Ferris wheel, rotating initially at an angular speed of 0.500 rad/s, accelerates over a 7.00-s interval at a rate of 0.040 0 rad/s . What angular displacement does the Ferris wheel undergo in this 7-s interval? a. 4.48 rad b. 2.50 rad c. 3.00 rad d. 0.500 rad 89 Chapter 7, Rotational Motion and the Law of Gravity 7.3 Relations Between Angular and Linear Quantities 16. A ventilation fan has blades 0.25 m in radius rotating at 20 rpm. What is the tangential speed of each blade tip? a. 0.02 m/s b. 0.52 m/s c. 5.0 m/s d. 20 m/s 17. A 0.30-m-radius automobile tire accelerates from rest at a constant 2.0 rad/s over a 5.0-s interval. What is the tangential component of acceleration for a point on the outer edge of the tire during the 5-s interval? 2 a. 33 m/s b. 6.7 m/s 2 c. 0.60 m/s 2 2 d. 0.30 m/s 18. A point on the rim of a 0.30-m-radius rotating wheel has a tangential speed of 4.0 m/s. What is the tangential speed of a point 0.20 m from the center of the same wheel? a. 1.0 m/s b. 1.3 m/s c. 2.7 m/s d. 8.0 m/s 19. A 0.15-m-radius grinding wheel starts at rest and develops an angular speed of 12.0 rad/s in 4.0 s. What is the average tangential acceleration of a point on the wheel’s edge? 2 a. 0.45 m/s b. 6.8 m/s 2 c. 28 m/s 2 2 d. 14 m/s 20. The end of the cutting cord on a gas-powered weed cutter is 0.15 m in length. If the motor rotates at the rate of 20 rev/s, what is the tangential speed of theend of thecord? a. 628 m/s b. 25 m/s c. 19 m/s d. 63 m/s 90 Chapter 7, Rotational Motion and the Law of Gravity 21. A bucket in an old well is hoisted upward by a rope which winds up on a cylinder having a radius of 0.050 m. How many rev/s must the cylinder turn if the bucket is raised at a speed of 0.15 m/s? a. 3.0 rev/s b. 1.5 rev/s c. 0.48 rev/s d. 0.24 rev/s 22. Consider a point on a bicycle wheelas the wheel makes exactly four complete revolutions about a fixed axis. Compare the linear and angular displacement of thepoint. a. Both are zero. b. Only the angular displacement is zero. c. Only the linear displacement is zero. d. Neither is zero. 23. Consider a point on a bicycle wheel as the wheel turns about a fixed axis, neither speeding up nor slowing down. Compare the linear and angular velocities of the point. a. Both are constant. b. Only the angular velocity is constant. c. Only the linear velocity is constant. d. Neither is constant. 24. Consider a point on a bicycle wheel as the wheel turns about a fixed axis, neither speeding up nor slowing down. Compare the linear and angular accelerations of the point. a. Both are zero. b. Only the angular acceleration is zero. c. Only the linear acceleration is zero. d. Neither is zero. 25. Calculate the linear speed dueto the Earth’s rotation for a person at the equator of theEarth. 6 The radius of the Earth is 6.40 × 10 m. a. 74.0 m/s b. 233 m/s c. 465 m/s d. 73.0 m/s 26. Calculate the linear speed dueto the Earth’s rotation for a person at a point on its surface o 6 located at 40 N latitude. The radius of the Earth is 6.40 × 10 m. a. 299 m/s b. 357 m/s c. 390 m/s d. 465 m/s 91 Chapter 7, Rotational Motion and the Law of Gravity 7.4 Centripetal Acceleration 27. A ventilation fan has blades 0.25 m longrotating at 20 rpm. What is the centripetal acceleration of a point on the outer tip of a blade? a. 1.1 m/s 2 2 b. 0.87 m/s c. 0.55 m/s 2 2 d. 0.23 m/s 2 28. A 0.30-m-radius automobile tire accelerates from rest at a constant 2.0 rad/s . What is the centripetal acceleration of a point on theouter edge of thetire after 5.0 s? 2 a. 300 m/s b. 33 m/s 2 2 c. 30 m/s 2 d. 3.0 m/s 29. A 0.40-kg mass, attached to the end of a 0.75-m string, is whirled around ina circular horizontal path. If the maximumtension that the string can withstand is 450 N, then what maximum speedcan the mass have if the string is not to break? a. 370 m/s b. 22 m/s c. 19 m/s d. 29 m/s 30. A point on the rim of a 0.25-m-radius fan blade has centripetal acceleration of 0.20 m/s . Find 2 the centripetal acceleration of a point 0.05 m from the center of the same wheel. a. 0.01 m/s 2 2 b. 0.02 m/s c. 0.04 m/s 2 d. 0.08 m/s 2 31. A point on the rim of a 0.25-m-radius rotating wheel has a centripetal acceleration of 4.0 m/s . 2 What is the angular speed of the wheel? a. 1.0 rad/s b. 2.0 rad/s c. 3.2 rad/s d. 4.0 rad/s 92 Chapter 7, Rotational Motion and the Law of Gravity 32. A point on the rim of a 0.15-m-radius rotating disk has a centripetal acceleration of 5.0 m/s . 2 What is the angular speed of a point 0.075 m from the center of the disk? a. 0.89 rad/s b. 1.6 rad/s c. 3.2 rad/s d. 5.8 rad/s 33. When a point on the rim of a 0.30-m-radius wheel experiences a centripetal acceleration of 4.0 2 m/s , what tangential acceleration does that point experience? a. 1.2 m/s 2 2 b. 2.0 m/s c. 4.0 m/s 2 d. Cannot determine with the information given. 34. A 0.150-m-radius grindingwheel, starting at rest, develops an angular speed of 12.0 rad/s in a time interval of 4.00 s. What is the centripetal acceleration of a point 0.100 m from the center when the wheel is moving at an angular speed of 12.0 rad/s? a. 0.450 m/s 2 2 b. 7.20 m/s c. 14.4 m/s 2 2 d. 28.8 m/s 35. The distance from the center of a Ferris wheel to a passenger seat is 12 m. What centripetal acceleration does a passenger experience when the wheel’s angular speed is 0.50 rad/s? a. 16.9 m/s 2 2 b. 9.0 m/s 2 c. 3.0 m/s d. 6.0 m/s 2 36. What centripetal force does an 80-kg passenger experience when seated 12 m from the center of a Ferris wheel whoseangular speed is 0.50 rad/s? a. 484 N b. 720 N c. 914 N d. 240 N 37. A 0.400-kg object is swung in a circular path and in a vertical plane on a 0.500-m-length string. If the angular speed at the bottom is 8.00 rad/s, what is the tensionin the string when the object is at the bottom of the circle? a. 5.60 N b. 10.5 N c. 16.7 N 93 Chapter 7, Rotational Motion and the Law of Gravity d. 19.6 N 38. A 0.30-kg rock is swungin a circular path and in a vertical plane on a 0.25-m-length string. At the top of the path, the angular speed is 12.0 rad/s. What is the tension in the string at that point? a. 7.9 N b. 16 N c. 18 N d. 83 N 39. A 1 500-kg car rounds an unbanked curve with a radius of 52 m at a speed of 12 m/s. What minimum coefficient of friction must exist between the road and tires to prevent the car from 2 slipping? (g = 9.8 m/s ) a. 0.18 b. 0.30 c. 0.28 d. 0.37 40. At what angle (relative to the horizontal) should a curve 52 m in radius be banked if no friction is required to prevent the car from slipping when traveling at 12 m/s? (g = 9.8 m/s ) 2 a. 28° b. 32° c. 16° d. 10° 41. At what speed will a car round a 52-m-radius curve, banked at a 45° angle, if no frict2on is required betweenthe road and tires to prevent the car from slipping? (g = 9.8 m/s ) a. 27 m/s b. 17 m/s c. 23 m/s d. 35 m/s 42. A roller coaster, loaded with passengers, has a mass of 2 000 kg; the radius of curvature of the track at the bottom point of the dip is 24 m. If the vehicle has a speed of 18 m/s at this point, 2 what force is exerted on the vehicle by the track? (g = 9.8 m/s ) a. 2.3 × 10 N 4 b. 4.7 × 10 N c. 3.0 × 10 N d. 1.0 × 10 N 94 Chapter 7, Rotational Motion and the Law of Gravity 43. Consider a point on a bicycle tire that is momentarily in contact with the ground as the bicycle rolls across the ground with constant speed. The direction for the acceleration for this point at that moment is: a. upward. b. down toward the ground. c. forward. d. at that moment the acceleration is zero. 44. Consider a child who is swinging. As she reaches the lowest point in her swing: a. the tension in the rope is equal to her weight. b. the tension in therope is equal to her mass times her acceleration. c. her acceleration is downward at 9.8 m/s . d. none of the above. 45. What angular speed (inrevolutions/second) is needed for a centrifuge to produce an acceleration of 1 000 g at a radius arm of 15.0 cm? a. 40.7 rev/s b. 75.4 rev/s c. 81.4 rev/s d. 151 rev/s 46. An airplane in a widesweeping “outside” loop can create zero gees insidethe aircraft cabin. What must be the radius of curvature of theflight path for an aircraft movingat 150 m/s to create a condition of “weightlessness” insidethe aircraft? a. 1 150 m b. 1 800 m c. 2 300 m d. 3 600 m 47. A cylindrical space colony 8 kmin diameter and 30 km long has been proposed as living quarters for future space explorers. Such a habitat would havecities, land and lakes on the inside surface and air and clouds in the center. All this would be held in place by the rotation of the cylinder about the longaxis. How fast would such a cylinder have to rotate to produce a 1-g gravitational field at the walls of the cylinder? a. 0.05 rad/s b. 0.10 rad/s c. 0.15 rad/s d. 0.20 rad/s 95 Chapter 7, Rotational Motion and the Law of Gravity 48. The Earth is 93 million miles (mi) from the Sun and its period of revolution is 1 year = 3.15 × 7 10 s. What is the acceleration of theEarth in its orbit about the Sun? 2 a. 18.6 mi/s b. 9.3 × 10 mi/s 2 −6 2 c. 13.6 × 10 mi/s d. 3.7 × 10 mi/s 2 49. A wheel is rotated about a horizontal axle at a constant angular speed. Next it is rotated in the opposite direction with the sameangular speed. The acceleration at a point on the top of the wheelin the second case as compared to the acceleration in the first case: a. is in the same direction. b. is in the opposite direction. c. is upward. d. is tangential to the wheel. 7.5 Newtonian Gravitation 50. An object of mass 0.50 kg is transported to the surface of Planet X where the object’s weight is 6 measured to be 20 N. The radius of the planet is 4.0 × 10 m. What is the mass of Planet X? (G = 6.67 × 10 −11N ⋅ m /kg )2 a. 13 × 10 kg9 22 b. 17 × 10 kg 24 c. 9.6 × 10 kg d. 21 × 10 kg5 51. An object of mass 0.50 kg is transported to the surface of Planet X where theobject’s weight is 6 measured to be 20 N. The radius of the planet is 4.0 × 10 m. What free fall acceleration will the 0.50-kg object experiencewhen at the surface of Planet X? 2 a. 48 m/s b. 20 m/s 2 2 c. 16 m/s d. 40 m/s 2 52. An object of mass 0.50 kg is transported to the surface of Planet X where the object’s weight is 6 measured to be 20 N. The radius of the planet is 4.0 × 10 m. What free fall acceleration will the 0.50-kg object experience when transported to a distance of 2.0 × 10 m from the surface of this planet? 2 a. 90 m/s b. 20 m/s 2 2 c. 13 m/s d. 18 m/s 2 96 Chapter 7, Rotational Motion and the Law of Gravity 53. An Earth satelliteis orbiting at a distance from the Earth’s surface equal to one Earth radius (4 000 miles). At this location, the acceleration due to gravity is what factor times the value of g at the Earth’s surface? a. There is noacceleration since the satellite is in orbit. b. 2 c. 1/2 d. 1/4 54. If a planet has 3 times the radius of the Earth, but has the same density as 2he Earth, what is the gravitational acceleration at the surface of the planet? (g = 9.8 m/s ) 2 a. 29.4 m/s b. 88.2 m/s 2 c. 265 m/s 2 2 d. 3.27 m/s 55. If a planet has a radius 20% greater than that of the Earth but has the samemass as the Earth, what is the acceleration dueto gravity at its surface? a. 14 m/s 2 2 b. 12 m/s c. 8.2 m/s 2 2 d. 6.8 m/s 56. The acceleration due to gravity at the surface of Planet X is 10 m/s . What is the acceleration due to gravity at an altitude of 3000 km above thesurface of this planet? a. 10 m/s 2 2 b. 8.0 m/s 2 c. 4.4 m/s d. More information is needed. 57. An object when orbiting the Earth at a height of three Earth radii from the center of the Earth has a weight of 1.00 N. What is the object’s mass? (g at the surface of theEarth is 9.8 m/s ) 2 a. 0.102 kg b. 0.306 kg c. 0.92 kg d. 1.0 kg 58. Somewhere between the Earth and the Moonis a point where the gravitational attraction of the Earth is canceled by thegravitational pull of the Moon. The mass of the Moon is 1/81 that of the Earth. How far from the center of the Earth is this point? a. 8/9 the way to the Moon b. 9/10 the way to the Moon c. 3/4 the way to the Moon 97 Chapter 7, Rotational Motion and the Law of Gravity d. 80/81 the way to the Moon 59. A satelliteis in a circular orbit about the Earth at a distance of oneEarth radius a6ove the surface. What is the speed of the satellite? (The radius of the Earth is 6.4 × 10 m, and G = 6.67 × 10 −11N ⋅ m /kg .) a. 2 800 m/s b. 4 200 m/s c. 5 600 m/s d. 16 800 m/s 60. A careful photographic survey of Jupiter’s moon Io by the spacecraft Voyager 1 showed active volcanoes spewing liquid sulfur to heights of 70 km above the surface of this moon. If the value of g on Io is 2.0 m/s , estimate the speed with which the liquid sulfur left the volcano. a. 260 m/s b. 530 m/s c. 790 m/s d. 970 m/s 61. If the mass of Mars is 0.107 times that of Earth, and its radius is 0.530 that of Earth, estimate 2 the gravitational acceleration g at the surface of Mars. (g earth 9.80 m/s ) a. 2.20 m/s 2 2 b. 3.73 m/s 2 c. 4.20 m/s d. 5.50 m/s 2 62. The escape speed fromthe surface of the Earth is 11.2 km/s. Estimate the escape speed for a spacecraft from the surface of theMoon. The Moonhas a mass 1/81 that of Earth and a radius 0.25 that of Earth. a. 2.5 km/s b. 4.0 km/s c. 5.6 km/s d. 8.7 km/s 63. Geosynchronous satellites orbit the Earth at a distance of 42 000 km fromthe Earth’s center. Their angular speed at this height is the sameas the rotation rate of the Earth, so they appear stationary at certain locations inthe sky. What is the force acting on a 1 500-kg satellite at this height? a. 85 N b. 333 N c. 404 N d. 457 N 98 Chapter 7, Rotational Motion and the Law of Gravity 64. At an altitude of 4 times theradius of the earth, the acceleration due to gravity is a. g/2. b. g/4. c. g/16. d. not given. 7.6 Kepler’s Laws 65. An asteroid has a perihelion (the orbit’s closest approach to the sun) of 1.5 AU and a period of revolution of 8.0 y. What is its greatest distance from the sun (its aphelion)? a. 8.0 AU b. 6.5 AU c. 4.0 AU d. 2.5 AU 66. Two satellites are monitored as they orbit the Earth; satellite X is eight times as far from the Earth’s center as is satellite Y. From Kepler’s third law one may conclude that the period or revolution of X is what factor times that of Y? a. 1/2 b. 2.0 c. 4.0 d. 22.6 67. At what location does an artificial Earth satellite inelliptical orbit have its greatest speed? a. nearest the Earth b. farthest from the Earth c. between Earth and Moon d. betweenEarth and Sun 68. An asteroid in orbit about the sun has a linear speed of 4 km/s when at a distance of closest approach d from the sun. What is its linear speed when it is at its greatest distance from the sun, a distance 2 d? a. 1 km/s b. 2 km/s c. 8 km/s d. 16 km/s 69. An artificial Earth satellite in an elliptical orbit has its greatest centripetal acceleration when it is at what location? a. nearest the Earth b. farthest fromthe Earth c. between Earth and Moon 99 Chapter 7, Rotational Motion and the Law of Gravity d. betweenEarth and Sun 70. Which of the following best describes the property of the period of orbital revolution for an Earth satellite? a. greater when the orbital radius is smaller b. greater when the orbital radius is larger c. independent of the orbital radius d. determined mainly by the satellite’s mass 71. Of the nine known planets in our solar system, the innermost is Mercury. When compared to the other planets in the system, Mercury has the: a. greatest centripetal acceleration. b. greatest period of revolution. c. smallest angular velocity. d. smallest tangential velocity. 72. According to Kepler’s second law, Halley’s Comet circles the Sun in an elliptical path with the Sun at one focus of the ellipse. What is at the other focus of the ellipse? a. nothing b. the Earth c. The comet itself passes through the other focus. d. The tail of the comet stays at the other ellipse. 73. For any object orbiting the Sun, Kepler’s Law may be writtenT = kr . If T is measured in years and r in units of the Earth’s distance from theSun, then k = 1. What, therefore, is the time (inyears) for Mars to orbit the Sun if its mean radius from the Sun is 1.5 times the Earth’s distance from the Sun? a. 1.8 years b. 2.8 years c. 3.4 years d. 4.2 years 74. In order for a satellite to be geosynchronous, its orbit must: a. go over the North and South Poles. b. be over the equator. c. be over a single longitude. d. emit television signals. 100 Chapter 7, Rotational Motion and the Law of Gravity 75. An asteroid is in orbit at 4 times the earth’s distance from the Sun. What is its period of revolution? a. one fourth year b. 4 years c. 8 years d. 16 years 76. Doubling the mean distance from the Sun results in changing the orbital period of revolution by what factor? a. 21/2 b. 2 3/2 c. 2 d. 22 101 Chapter 7, Rotational Motion and the Law of Gravity C HAPTER 7 - A NSWERS # Ans Difficulty # Ans Difficulty 1. C 1 39. C 2 2. C 1 40. C 2 3. C 1 41. C 2 4. A 2 42. B 3 5. B 2 43. A 1 6. D 2 44. D 2 7. B 1 45. A 2 8. C 2 46. C 2 9. D 2 47. A 2 10. B 2 48. D 2 11. B 1 49. A 1 12. D 1 50. C 3 13. B 2 51. D 2 14. D 2 52. D 3 15. A 2 53. D 2 16. B 1 54. A 2 17. C 1 55. D 2 18. C 2 56. D 2 19. A 2 57. C 2 20. C 2 58. B 3 21. C 2 59. C 2 22. C 2 60. B 2 23. B 2 61. B 3 24. B 2 62. A 3 25. C 2 63. B 3 26. B 3 64. D 3 27. A 2 65. B 3 28. C 2 66. D 2 29. D 2 67. A 1 30. C 2 68. B 2 31. D 2 69. A 2 32. D 2 70. B 1 33. D 2 71. A 1 34. C 2 72. A 1 35. C 2 73. A 2 36. D 2 74. B 1 37. C 3 75. C 2 38. A 3 76. C 2 102

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