A) 0.25 year B) 2.5 years C) 4 years D) 8 years E) 16 years

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1 Name: Date: 1. A ball is whirled on the end of a string in a horizontal circle of radius R at constant speed v. Complete the following statement: The centripetal acceleration of the ball can be increased by a factor of 4 by A) keeping the speed fixed and increasing the radius by a factor of 4. B) keeping the radius fixed and increasing the speed by a factor of 4. C) keeping the radius fixed and increasing the period by a factor of 4. D) keeping the radius fixed and decreasing the period by a factor of 4. E) keeping the speed fixed and decreasing the radius by a factor of The radius of the earth is 6400 km. An incoming meteorite approaches the earth along the trajectory shown. The point C in the figure is 6400 km above the earth's surface. The point A is located at the earth's center. At point C, what acceleration would the meteorite experience due to the earth's gravity? A) 9.8 m/s 2 toward A D) 5.0 m/s 2 toward B B) 2.5 m/s 2 toward A E) 5.0 m/s 2 toward A C) 2.5 m/s 2 toward B 3. A 0.25-kg ball attached to a string is rotating in a horizontal circle of radius 0.5 m. If the ball revolves twice every second, what is the tension in the string? A) 2 N B) 5 N C) 7 N D) 10 N E) 20 N 4. Consider a hypothetical planet in our solar system whose average distance from the Sun is about four times that of Earth. Determine the orbital period for this hypothetical planet. A) 0.25 year B) 2.5 years C) 4 years D) 8 years E) 16 years Page 1

2 5. A racecar is traveling at constant speed around a circular track. What happens to the centripetal acceleration of the car if the speed is doubled? A) The centripetal acceleration remains the same. B) The centripetal acceleration increases by a factor of 2. C) The centripetal acceleration increases by a factor of 4. D) The centripetal acceleration is decreased by a factor of one-half. E) The centripetal acceleration is decreased by a factor of one-fourth 6. Approximately one billion years ago, the Moon orbited the Earth much closer than it does today. The radius of the orbit was only km. Today, the radius is km. The orbital period was only s. The present period is s. Assume that the orbit of the Moon is circular. Calculate the ratio of the speed of the Moon in its ancient orbit to the speed that it has today. A) 15.8 B) 12.8 C) 10.2 D) 7.15 E) A 0.75-kg ball is attached to a 1.0-m rope and whirled in a vertical circle. The rope will break when the tension exceeds 450 N. What is the maximum speed the ball can have at the bottom of the circle without breaking the rope? A) 24 m/s B) 12 m/s C) 32 m/s D) 16 m/s E) 38 m/s 8. A satellite is placed in equatorial orbit above Mars, which has a radius of 3397 km and a mass MM = kg. The mission of the satellite is to observe the Martian climate from an altitude of 488 km. What is the orbital period of the satellite? A) s B) s C) s D) s E) s 9. A spaceship is in orbit around the earth at an altitude of miles. Which one of the following statements best explains why the astronauts experience weightlessness? A) The centripetal force of the earth on the astronaut in orbit is zero newtons. B) The pull of the earth on the spaceship is canceled by the pull of the other planets. C) The spaceship is in free fall and its floor cannot press upwards on the astronauts. D) The force of gravity decreases as the inverse square of the distance from the earth's center. E) The force of the earth on the spaceship and the force of the spaceship on the earth cancel because they are equal in magnitude but opposite in direction. Page 2

3 10. A certain string just breaks when it is under 25 N of tension. A boy uses this string to whirl a 2-kg stone in a horizontal circle of radius 3 m. The boy continuously increases the speed of the stone. At approximately what speed will the string break? A) 6 m/s B) 9 m/s C) 12 m/s D) 15 m/s E) 18 m/s 11. The Earth takes slightly less than one day to complete one rotation about the axis passing through its poles. The actual time is s. Given this information, what is the angular speed of the Earth about its axis? A) rad/s D) rad/s B) rad/s E) rad/s C) rad/s Use the following to answer question 12: A long thin rod of length 2L rotates with a constant angular acceleration of 10 rad/s 2 about an axis that is perpendicular to the rod and passes through its center. 12. What is the ratio of the angular speed (at any instant) of a point on the end of the rod to that of a point a distance L/2 from the end of the rod? A) 1:1 B) 1:2 C) 2:1 D) 4:1 E) 1:4 Use the following to answer question 13: A grindstone of radius 4.0 m is initially spinning with an angular speed of 8.0 rad/s. The angular speed is then increased to 10 rad/s over the next 4.0 seconds. Assume that the angular acceleration is constant. 13. What is the magnitude of the angular acceleration of the grindstone? A) 0.50 rad/s 2 B) 2.0 rad/s 2 C) 4.5 rad/s 2 D) 9.0 rad/s 2 E) 18 rad/s A bicycle wheel of radius 0.70 m is turning at an angular speed of 6.3 rad/s as it rolls on a horizontal surface without slipping. What is the linear speed of the wheel? A) 1.4 m/s B) 28 m/s C) 0.11 m/s D) 4.4 m/s E) 9.1 m/s 15. A spinning disc rotating at 130 rev/min slows and stops 31 s later. How many revolutions did the disc make during this time? A) 34 B) 67 C) 8.4 D) 17 E) 4.2 Page 3

4 Use the following to answer question 16: A wheel of radius 0.5 m rotates with a constant angular speed about an axis perpendicular to its center. A point on the wheel that is 0.2 m from the center has a tangential speed of 2 m/s. 16. Determine the tangential acceleration of the point that is 0.2 m from the center. A) 0.4 m/s 2 B) 2.0 m/s 2 C) 4.0 m/s 2 D) 10 m/s 2 E) zero m/s The original Ferris wheel had a radius of 38 m and completed a full revolution (2 radians) every two minutes when operating at its maximum speed. If the wheel were uniformly slowed from its maximum speed to a stop in 35 seconds, what would be the magnitude of the tangential acceleration at the outer rim of the wheel during its deceleration? A) m/s 2 B) m/s 2 C) 0.54 m/s 2 D) 1.6 m/s 2 E) 6.8 m/s A wheel, originally rotating at 126 rad/s undergoes a constant angular deceleration of 5.00 rad/s 2. What is its angular speed after it has turned through an angle of 628 radians? A) 15 rad/s B) 19 rad/s C) 98 rad/s D) 121 rad/s E) 150 rad/s Use the following to answer question 19: A long thin rod of length 2L rotates with a constant angular acceleration of 10 rad/s 2 about an axis that is perpendicular to the rod and passes through its center. 19. What is the ratio of the tangential speed (at any instant) of a point on the end of the rod to that of a point a distance L/2 from the end of the rod? A) 1:1 B) 1:2 C) 2:1 D) 4:1 E) 1:4 Use the following to answer question 20: A bicycle wheel of radius 0.70 m is rolling without slipping on a horizontal surface with an angular speed of 2.0 rev/s when the cyclist begins to uniformly apply the brakes. The bicycle stops in 5.0 s. 20. Through how many revolutions did the wheel turn during the 5.0 seconds of braking? A) 10 rev B) 2.0 rev C) 9.6 rev D) 5.0 rev E) 0.4 rev Page 4

5 21. A 3.0-kg ball moves in a straight line at 10 m/s as shown in the figure. At the instant shown, what is its angular momentum about the point P? A) 30 kg m 2 /s B) 90 kg m 2 /s C) 120 kg m 2 /s D) 150 kg m 2 /s E) zero kg m 2 /s 22. Consider the following four objects: a hoop a solid sphere a flat disk a hollow sphere Each of the objects has mass M and radius R. The axis of rotation passes through the center of each object, and is perpendicular to the plane of the hoop and the plane of the flat disk. Which object requires the largest torque to give it the same angular acceleration? A) the solid sphere D) the flat disk B) the hollow sphere E) both the solid and the hollow spheres C) the hoop 23. A string is tied to a doorknob 0.79 m from the hinge as shown in the figure. At the instant shown, the force applied to the string is 5.0 N. What is the torque on the door? A) 3.3 N m B) 2.2 N m C) 1.1 N m D) 0.84 N m E) 0.40 N m Page 5

6 24. A 3.0-kg ball and a 1.0-kg ball are placed at opposite ends of a massless beam so that the system is in equilibrium as shown. Note: The drawing is not drawn to scale. What is the ratio of the lengths, b/a? A) 2.0 B) 2.5 C) 3.0 D) 4.0 E) A hollow sphere of radius 0.25 m is rotating at 13 rad/s about an axis that passes through its center. The mass of the sphere is 3.8 kg. Assuming a constant net torque is applied to the sphere, how much work is required to bring the sphere to a stop? A) 1.0 J B) 3.8 J C) 13 J D) 25 J E) 38 J 26. The drawing shows the top view of a door that is 2 m wide. Two forces are applied to the door as indicated. What is the magnitude of the net torque on the door with respect to the hinge? A) 0 N m B) 5.0 N m C) 8.7 N m D) 10.0 N m E) 26.0 N m 27. Two equal spheres, labeled A and B in the figure, are attached to a massless rod with a frictionless pivot at the point P. The system is made to rotate clockwise with angular speed on a horizontal, frictionless tabletop. Sphere A collides with and sticks to another equal sphere that is at rest on the tabletop. Note: the masses of all three spheres are equal. What is the angular speed of the system immediately after the collision? A) B) 0.82 C) 0.60 D) 0.56 E) 0.29 Page 6

7 28. A solid sphere rolls without slipping along a horizontal surface. What percentage of its total kinetic energy is rotational kinetic energy? A) 33 % B) 50 % C) 12 % D) 75 % E) 29 % 29. A hollow cylinder of mass M and radius R rolls down an inclined plane. A block of mass M slides down an identical inclined plane. Complete the following statement: If both objects are released at the same time, A) the cylinder will reach the bottom first. B) the block will reach the bottom first. C) the block will reach the bottom with the greater kinetic energy. D) the cylinder will reach the bottom with the greater kinetic energy. E) both the block and the cylinder will reach the bottom at the same time. 30. A certain merry-go-round is accelerated uniformly from rest and attains an angular speed of 0.4 rad/s in the first 10 seconds. If the net applied torque is 2000 N m, what is the moment of inertia of the merry-go-round? A) 400 kg m 2 B) kg m 2 C) 5000 kg m 2 D) 800 kg m 2 E) This cannot be determined since the radius is not specified. Page 7

8 Answer Key 1. E 2. B 3. E 4. D 5. C 6. E 7. A 8. C 9. C 10. A 11. A 12. A 13. A 14. D 15. A 16. E 17. B 18. C 19. C 20. D 21. B 22. C 23. A 24. D 25. C 26. C 27. D 28. E 29. B 30. B Page 8