Base your answers to questions and on the 5.An …...Base your answers to questions 1 and 2 on the...

Base your answers to questions 1 and 2 on thefollowing situation.

An object weighing 10 N swings at the end of a ropethat is 0.72 m long as a simple pendulum. At thebottom of the of the swing, the tension in the string is12 N.

A) 0.6 m/s B) 1.2 m/sC) 2.0 m/s D) 2.4 m/sE) 7.2 m/s

1. What is the speed of the object at the bottom of theswing?

A) 2 m/s2 B) 4 m/s2C) 10 m/s2 D) 12 m/s2E) 22 m/s2

2. What is the magnitude of the centripetal accelerationat the bottom of the swing?

A) 2:1 B) 1:2 C) 3:1 D) :1 E) 1:

3. Two satellites (equal in mass) are in circular orbitaround the Earth. The distance to the Earth's center ofSatellite A is twice that of Satellite B. The ratio ofthe speed of Satellite A to Satellite B is

A) B)

C) D)

E)

4. Two satellites (equal in mass) are in a circular orbitaround the Earth. Satellite 1 is traveling at constantvelocity v 1. Satellite B is traveling at constantvelocity v 2. If Satellite A is at a distance r 1 from theEarth's center, the distance from Satellite B to theEarth's center is

A) 0B) 2

Tr 2C) 2 r

TD) 4 2r

T 2E) 4 2

Tr 2

5. An object moves at constant speed in a circular pathof radius r with a period of T. What is the object'sacceleration?

A) II onlyB) II and III onlyC) I and III onlyD) I, II, and IIIE) None of the above are accurate

6. An object is tied to a string and moves in a circularpath at constant speed. Which of the followingstatements are accurate?

I. The net force on the object is zero. II. The acceleration is zero.III. The acceleration is constant.

A) The velocity is constant.B) The acceleration is constant.C) The acceleration is constant, but the velocity

varies.D) The velocity is constant, but the acceleration

varies.E) Both the acceleration and velocity are constant.

7. An object is undergoing uniform circular motion.Which of the following statements is true?

A) 2 25 B) 2 25C) 2 D) 4E) 4 2 25

8. What is the centripetal acceleration of a ball swingingaround a string when it passes one revolution in 5seconds and the radius of its path is 1m?

A) v2

B) v

C) vD) 2vE) 4v

9. A ball attached to a string is whirled around ahorizontal circle of radius r with a tangential velocity v. If the radius is changed to 2r and the magnitude ofthe centripetal force is doubled the new speed is

A) 4 2R2 TB) 4 2R2 T2C) 4 2R2 T2D) 4 2R

T2E) 4 2R

T

10. A satellite orbits a planet at a radius R with a period T. What is the magnitude of its centripetalacceleration?

A) I, only B) III, onlyC) I and II, only D) I and III, onlyE) I, II, and III

11. A racecar, starting at rest, travels 3 times around aclosed track, and ends at rest. Which of thefollowing are true concerning this motion?

I. The total displacement is zeroII. The average speed is zeroIII. The average acceleration is zero

A) 12.5 m B) 25 mC) 50 m D) 62.5 mE) 100 m

12. An object moves, starting from rest, along africtionless track with a loop shown below.

What is the minimum height, h, of the track for theobject to make it completely around the circle?

A) always directed away from the center of thecircle

B) always directed toward the center of the circleC) always directed in the direction of the velocityD) inversely proportional to the radius of the circleE) zero

13. The centrifugal force felt by an object in uniformcircular motion is

A) F B) F C) F D) 2F E) 4F

14. A 60 kg adult and a 30kg child are passengers on arotor ride at an amusement park as shown in thediagram above. When the rotating hollow cylinderreaches a certain constant speed, v, the floor movesdownward. Both passengers stay "pinned" againstthe wall of the rotor, as shown in the diagram below.

The magnitude of the frictional force between theadult and the wall of the spinning rotor is F. What isthe magnitude of the frictional force between thechild and the wall of the spinning rotor?

A) 0.2 m B) 0.5 mC) 1 m D) 1.5 mE) 2 m

15. A particle travels in a circular path at constant speedwith a constant kinetic energy of 20 J. If the netforce on the particle is 40 N, what is the radius of theparticle's path?

A) 40 JB) 60 JC) 120 JD) 140 JE) Cannot be determined from the given

information.

16. A particle travels in a circular path of radius 4 m atconstant speed. The net force on the particle is 60 N.The kinetic energy of the particle is

Base your answers to questions 17 and 18 on thefollowing situation.

An engineer wishes to design a roller coaster so thatthe cars will not fall when they are at the top of theircircular path.

A) 5 m B) 10 m C) 20 m D) 40 m E) 80 m

17. A 500 kg roller coaster car is designed to travel at 20m/s at the top of the circle. The engineer wants tomake the circle as large as possible while still beingat least one quarter the maximum radius for safetyreasons. How large can the radius of the circle be?

A) The velocity of the cars as the pass the top ofthe circle.

B) The radius of the circular track.C) The mass of the cars.D) The distance from the top of the circle to the

bottom.E) The acceleration due to gravity.

18. Which of the following will have no effect onwhether the cars remains on the track?

Base your answers to questions 19 and 20 on the following situation.

An object with a mass of 5 kg is attached to a 1 meterlong rope and whirled in a vertical circle.

A) 1 m/s B) 2 m/sC) 4 m/s D) 5 m/sE) 10 m/s

19. Of the following, which is the greatest speed of theobject for which the rope would become slack at thetop of its circular path?


20. At the bottom of its path, the rope has a tension of 95N. The object is moving most nearly

A) 2m 2r T

B) 4m 2r T 2

C) 2m 2r T 2

D) 4m 2r T

E) 4m r T 2

21. A ball of mass M is revolving on a string on ahorizontal surface with a radius of R and a period of T. What is the tension in the string?

A) They are in opposite directions.B) They are always equal in magnitude.C) They are perpendicular in direction.D) They are both tangent to the path of motion.E) They are both directed toward the center of the

circle.

22. Which of the following is true of the velocity andacceleration vectors of an object moving with auniform speed in a circular path?

A) B)

C) D)

23. The diagram below shows a satellite of mass m orbiting Earth in a circular path of radius R.

If a centripetal force Fc is acting on the satellite,then its speed is equal to

A) A B) B C) C D) D E) E

24. A ball rolls down a curved ramp as shown in thediagram below. Which dotted line best representsthe path of the ball after leaving the ramp?

A) 0.5 m/s B) 1 m/sC) 2.5 m/s D) 5 m/sE) 25 m/s

25. An 10 kg object moving in a horizontal circle ofradius 5 m experiences a centripetal force of 50 N.What is the velocity of the object?

A) B)C) D)

E)

26. A small block of mass M is traveling on a trackwhere a loop of radius R exists.

What minimum speed is needed to keep the block onthe track?


27. What is the maximum speed a vehicle can travelalong a circular turn without leaving the road, if theturn has a radius of 50 m and the coefficient of staticfriction between the road and the tires is 0.20?

A) the diameter of the curve.B) the acceleration due to gravity.C) the mass of the car.D) the coefficient of kinetic friction between the

road and the tires.E) the surface of the curve.

28. The maximum speed a car can travel around anunbanked curve depends on all of the following EXCEPT

A) RMg B) RgC) 625/Mg D) 625/RgE) 625/RMg

29. A car of mass M is traveling around an unbanked,rough, and circular road with a radius of R at a speedof 25 m/s. What is the minimum coefficient ofkinetic friction required to allow the car to safelytravel around the turn?

A) 5 m/s B) 7.5 m/sC) 10 m/s D) 25 m/sE) 16 m/s

30. A vehicle of mass 3000 kg travels along anunbanked circular turn without leaving the road. Ifthe turn has a radius of 10 m, and the coefficient ofstatic friction between the road and the tires is 0.25,what is the maximum speed the vehicle can travelwithout slipping?

Base your answers to questions 31 and 32 on thediagram below.

A horizontal turntable rotates with a constant rate.As viewed from above, an object on the turntablemoves clockwise in a circle.

A) To the Left B) To the rightC) Down D) UpE) Up and to the left

31. Which of the following best describes the directionof the frictional force on the object?

A) Down and to the leftB) DownC) Down and to the rightD) To the leftE) To the right

32. Which of the following best describes the directionof the velocity of the object when it is in the positionshown?

A) 0 B) Ig/2r2C) Ig/r2 D) 2Ig/r2E) 2Ig/r

33. Base your answer to the following question on thediagram below which shows a uniform discconnected to a massless string of tension T.

What is T if the object is initially at rest?

A) Lsin B) Lcos C) L D) Ltan E) L

34. A massless rod is positioned on a frictionless pivotas shown. A force with magnitude F is applied at anangle , a distance L from the pivot. At whatdistance x must the same force F be appliedperpendicular to the rod such that the net torque onthe rod is zero?

A) 4:1 B) 2:1 C) 1:1 D) 1:2 E) 1:4

35. A rod of uniform material is balanced over a pivotwith masses m and M positioned such that thesystem is in static equilibrium. If the mass M is adistance d from the pivot, and the mass m is adistance from the pivot, what is the ratio of M to m?

A) 3 kg B) 4 kg C) 6 kg D) 8 kg E) 12 kg

36. To measure the weight of the cat, a person places a100 N box and a 60 N box from the ends of auniform pole that is pivoted at its center. The systembalances when the cat stands at a point of the rodslength from the 60 N box. What is the approximatemass of the cat?

A) 2TgB) 2T

gC) T

gD) T

2gE) 2g

T

37. The rod in the figure above is uniform, and thetension in the string is T. The mass of the rod is

A) mgsin B) mgsin

2C) mgcos

2D) mg

2cos E) mg

2sin

38. If the rod in the figure above is uniform with mass m, what is the tension in the supporting string?

A) mgR2 R1

B) mgR1 R2

C) mg(R1+R2) R1

D) mgR2 (R1+R2)

E) mgR1 (R1+R2)

39. The diagram above shows a stick of uniform densitywith length 2L and mass m supported near each endby upward forces. Find the magnitude of the force adistance R1 away from the center of the stick if thestick is balanced in a horizontal position.

A) mgL 2xcos

B) mgx 2Lsin

C) mgx 2(L–x)sin

D) mgL (L–x)sin

E) mgL 2(L–x)cos

40. The diagram above shows a massless pole of length L that supports a mass m being held horizontallyagainst a tower by a wire that makes an angle withthe horizontal pole. The wire is connected to thepole at a distance x from the free end of the pole.The mass is attached by a massless string at the freeend of the pole. For the pole to remain horizontal,the tension in the wire must be

A) B) C) D) E) 2L

41. In the diagram above, two masses, one with mass m,the other with mass M = 2m are resting on a uniformplank of length L that pivots at its midpoint. If themass m is at the far end of the plank, how far awayfrom the pivot should the mass M be to balance theplank in a horizontal position shown?

A) mgsin

B) mgcos

C) mgcos

D) mgsin

E) mgsin cos

42. In the diagram above a mass m is attached by amassless string to a stationary arm at an angle fromthe horizontal. If the net torque of the mass on thearm is , find the length of the lever arm.

A) 0 mB) 2 mC) 2 D) 6 mE) To the end of the beam

43. A person of mass 60 kg is walking down a 10 m, 100kg beam supported by two pillars, one at the head ofthe beam and one 3 m away from the center of thebeam.

How far down the beam can the person walk beforethe beam begins to tip? (Consider the origin to bethe left end of the beam.)

Base your answers to questions 44 and 45 on the following information.

A uniform rod of length L is placed into outer space with the following forces acting on it:• 5F upwards from its center of mass.• F 45 degrees downwards

A) X: Y:

B) X: Y: F(9– )

C) X: ( )2Y: 7F

D) X: F(9 – )Y:

E) X: F(9 – )Y:

44. What is the magnitude of the force needed to bring this object into translational equilibrium?

A) It will rotate Clockwise.B) It will rotate Counter-Clockwise.C) It will rotate in dynamic equilibrium.D) It will not rotate, it will only move upwards.E) It will not rotate it will only move downwards.

45. If this object is to rotate, which way would it be?

A) M2

B) M3

C) MD) 3M

2E) 2M

46. A uniform wooden board of mass 10 M is held up bya nail hammered into a wall. A block of mass M rests away from the pivot. Another block of acertain mass is hung a distance The system is instatic equilibrium.

What is the measure of the mass labeled "?" ?

A) it is in dynamic equilibrium.B) it is in static equilibrium.C) it is rotating.D) it is translating.E) its mechanical energy is negative.

47. When an object is experiencing a net torque

A) work B) energyC) speed D) torqueE) distance

48. Which of the following is not a scalar quantity?

Base your answers to questions 49 and 50 on thepicture below, which represents two objects, one ofmass 12 kg and one of mass m, hung from the endsof a stick with negligible mass, that is 80 centimeterslong and has marks every 10 centimeters as shownbelow.


49. If m = 7.2 kg, at what point should the rod bepivoted to remain horizontal?

A) 7.2 kg B) 7.5 kgC) 12 kg D) 20 kgE) 24 kg

50. If the stick remains horizontal when pivoted at point B, what is the mass of block m?

A) force B) torqueC) power D) momentumE) velocity

51. The newton•meter is a measure of

Base your answers to questions 52 and 53 on thepicture below, which represents a rigid uniform rodwith a mass of 6kg and a length of 1.0 m is pivotedon the right end. It is held in equilibrium by anupward force of 40 N.

A) 10 N B) 20 NC) 40 N D) 60 NE) 100 N

52. What force is applied to the rod by the pivot?

A) 10 cm B) 20 cmC) 25 cm D) 40 cmE) 50 cm

53. How far from the left end of the rod should the forcebe placed to maintain equilibrium?

A) 6F upwards B) 2F upwardsC) 0 D) 2F downwardsE) 6F downwards

54. A bar of length 3d is pivoted in the center as shown.At each of its ends a force of magnitude F is appliedin the directions indicated by the arrows.

What force must be applied at point X to keep therod in rotational equilibrium?

A) 2 rad/s B) 4 rad/sC) 8 rad/s D) 12 rad/sE) 16 rad/s

55. If an object of radius 2 m that experiences a constantangular acceleration starting from rest, rotates 18rads in 3 s, what is its angular velocity after 2 s?

A) 2.5 rad/s2 B) 5 rad/s2C) 7.5 rad/s2 D) 10 rad/s2E) 15 rad/s2

56. If an object of radius 3 m that experiences a constantangular acceleration starting from rest, rotates 10rads in 2 s, what is its angular acceleration?

A) B) C) D) E)

57. What is an expression for centripetal force acting onan object of mass m with uniform circular motion interms of angular velocity?

A) 8 m B) 10 m C) 24 m D) 30 m E) 64 m

58. How far does a point on the edge of a wheel with radius 3 m travel in the first 2 seconds of motion ifthe angular velocity is given by the equation w(t) = 3t +2?

A) 2 m/s B) 2 rad/sC) 4 m/s D) 4 rad/sE) 8 m/s

59. A wheel of radius 2 m moving at 2 rad/s accelerates to 4 rad/s in 2 s. What is the change in themagnitude of the linear velocity of a point on theedge of the wheel after this acceleration?

A) /8 m/s2 B) /4 rad/s2C) 1/8 rad/s2 D) 1/4 m/s2E) /2 rad/s2

60. If a rotating object starts at rest and completes onerotation in 4 s, what is its angular accelerationassuming its angular acceleration is constant?

A) 1 B) 1/r C) r D) r2 E) 1/r2

61. What is the ratio of angular velocity to linearvelocity?

A) 3 rad/s2 B) 6 rad/s2C) 7.5 rad/s2 D) 8 rad/s2E) 12 rad/s2

62. A tire spinning at 8 m/s uniformly accelerates to 20m/s in 4 s. Its radius is 40 cm. What is the angularacceleration of a pebble stuck in the tire during thisinterval?

A) 100° B) 125° C) 250° D) 300° E) 375°

63. A tire spinning at 5 m/s uniformly accelerates to 10m/s in 5 s. Its radius is 10 cm. Through what anglewill a pebble stuck in the tire revolve during thisinterval?

A) 6 m B) 9 m C) 12 m D) 18 m E) 30 m

64. A wheel spinning at 3 m/s uniformly accelerates to 6m/s in 4 s. Its radius is 20 cm. How far around thewheel will a speck of dust travel during that interval?

A) 0.25 rad/s2 B) 0.5 rad/s2C) 1 rad/s2 D) 1.25 rad/s2E) 2.5 rad/s2

65. A sphere at rest begins to spin with constant angularacceleration. When its angular displacement is 10radians, its angular velocity is 5 radians per second.What is its angular acceleration?

A) w2r B) v2r C) w2/r D) v2/r E) rw

66. What is an expression for centripetal acceleration interms of angular speed?

A) 1 rad/s2 B) 2 rad/s2C) 4 rad/s2 D) 6 rad/s2E) 8 rad/s2

67. A pebble is stuck in a tire of radius 0.25 m travelingat 4 m/s. The tire accelerates constantly up to 8 m/sin 4 seconds. What is the angular acceleration of thepebble during those 4 seconds?

A) 10 radians B) 20 radiansC) 30 radians D) 40 radiansE) 50 radians

68. A wheel begins at rest on top of an incline plane. Itrolls for 5 seconds until it reaches a speed of 4radians/second. Assuming constant acceleration,what is its angular displacement?


69. A disk of radius 3 m rotates at an angular velocity of4 radians per second. How fast does a point on theedge of the disk travel?

A) Zero B) –3 m/s2C) – m/s2 D) m/s2

E) 3 m/s2

70. The angular velocity of a rotating disk with a radiusof 2 m decreases from 6 radians per second to 3radians per second in 2 seconds. What is the linearacceleration of a point on the edge of the disk duringthis time interval?

A) 2 /5 B) 5 /2 C) 2 D) 5 E) 10

71. A rotating, rigid body takes 5 s to complete onerevolution. What is its average angular velocity interms of radians per second?

A) one of the endsB) at its center, l/2C) at its center of massD) at the point with the highest densityE) the moment of inertia is the same for any

location

72. A rod has non uniform mass distribution, a length l, and a mass m. If it is rotated around an axis that isperpendicular to its length, at what location of thisaxis will the rod have the smallest moment ofinertia?

A) B) C) D) E)

73.

A) I B) I/mdC) I – md D) I – md2E) I + md2

74. An object of mass m has a moment of inertia I whenit is rotated about its center of mass. What is itsrotational inertia if it is rotated about an axis that is adistance d from its center of mass?

A) Fr B) Fr/ C) /Fr D) r /F E) F /r

75. A force F is exerted on a rod at a distance r from itsaxis of rotation. If the rod experiences an angularacceleration of , what is the moment of inertia ofthe rod about this axis?

A) 6m B) 11m C) 16m D) 22m E) 26m

76. Base your answer to the following question on thediagram below.

What is the total rotational inertia of the systemwhen it is rotated about the origin?

A) 4m B) 6m C) 11m D) 13m E) 17m

77. Base your answer to the following question on thediagram below.

What is the moment of inertia of the system ofparticles if it is rotated about the origin?

A) 1:1 B) 2:5 C) 5:2 D) 4:5 E) 5:4

78. What is the ratio of the moment of inertia of acylinder of mass m and radius r to a the moment ofinertia of a sphere of the same mass and sameradius?

A) 1:1 B) 1:2 C) 2:1 D) 1:4 E) 4:1

79. What is the ratio of the moment of inertia of acylinder of mass m and radius r to a the moment ofinertia of a hoop of the same mass and same radius?

A) 1:1 B) 3:4 C) 2:5 D) 5:2 E) 4:3

80. What is the ratio of the moment of inertia of a solidsphere of mass m and radius r to a the moment ofinertia of a hoop of the same mass and same radius?

A) the net force on the carB) the moment of inertia of the car around a given

axisC) the work done by friction on the carD) the work done by gravity on the carE) the impulse imparted to the car by the normal

force

81. Which of the following quantities is non-zero for acar parked on a hill?

A) Zero B) 2 m/sC) 4 m/s D) 6 m/sE) 10 m/s

82. A solid cylinder of radius .2 m and mass 2 kg is atrest at a height 1.2 m at the top of an inclined planemaking an angle 60° with the horizontal. Assumingno slipping, what is the speed of the cylinder at thebottom of the incline?

A) angleB) angular velocityC) angular accelerationD) torqueE) moment of inertia

83. Mass is the translational analog of the

A) g/3 B) 5g/14C) 5g/7 D) 2g/3E) g

84. A solid sphere of mass M and radius R rolls withoutslipping down an inclined plane whose incline anglewith the horizontal is 30°. What is the accelerationof the sphere’s center of mass?

A) .2g B) .4g C) .6g D) .8g E) g

85. A block mass 3 kg is hung from a pulley of radius Rand mass 4 kg and is allowed to fall. What is theacceleration of the block?

A) 2:5 B) 1:2 C) 4:5 D) 5:4 E) 5:2

86. What is the ratio of the moment of inertias for a soliddisk and solid sphere with the same mass and sameradius?

A) .125 kgm2 B) .25 kgm2

C) .5 kgm2 D) 2.5 kgm2

E) 5 kgm2

87. What is the moment of inertia for a solid sphere witha radius of .5 meters and a mass of 5 kg?

A) .4 kgm2 B) .5 kgm2

C) .6 kgm2 D) .7 kgm2

E) .8 kgm2

88. What is the moment of inertia for a solid disk with adiameter of .8 meters and a mass of 5 kg?

A) Angular velocityB) Translational velocityC) Moment of inertiaD) TorqueE) Angular momentum

89. The parallel axis theorem is used to calculate

A) cylinderB) sphereC) hoopD) all have the sameE) not enough information

90. Which of the following objects has the leasttranslational kinetic energy at the bottom of theincline if they all have the same mass and radius?


91. Which of the following objects has the greatesttranslational energy at the bottom of the incline ifthey all have the same mass and radius?


92. Which of the following objects has the leastrotational kinetic energy at the bottom of the inclineif they all have the same mass and radius?


93. Which of the following objects has the greatestrotational kinetic energy at the bottom of the inclineif they all have the same mass and radius?


94. Which of the following objects has the least kineticenergy at the bottom of the incline if they all havethe same mass and radius?

A) and x B) w and vC) a and a D) I and ME) t and W

95. Which of the following rotational-translational pairsis incorrect?

A) 1 J B) 1.5 J C) 2 J D) 2.5 J E) 3 J

96. What is the total kinetic energy of a hoop of radius 1m and mass 2 kg that rolls at an angular velocity of 1rad/s?

A) 1:1 B) 1:2 C) 2:1 D) 1:4 E) 4:1

97. Two equal forces do W Joules of work on cylinderand a hoop of the same radius and same mass. Whatis the ratio of the total kinetic energy of the cylinderto the total kinetic energy of the hoop after this workhas been done?

A) 80 J B) 90 J C) 170 J D) 225 J E) 305 J

98. A solid sphere of radius 5 m and mass 2 kg rolls atan angular velocity of 3 rad/s on a surface at a heightof 4 m above the ground. What is the potentialenergy of the system?

A) 9 J B) 30 J C) 90 J D) 225 J E) 450 J

99. A solid sphere of radius 5 m and mass 2 kg rolls atan angular velocity of 3 rad/s. What is its rotationalkinetic energy?

A) a/t B) a/t2C) I a2/t D) I a2/t2E) I a/t

100. A spinning object with moment of inertia I increases in angular speed from = 0 to a in tseconds.

What is the average torque on the wheel during thisinterval t?

101. Base your answer to the following question on theinformation below.

A spinning object with moment of inertia I increases in angular speed from w = 0 to w a in t seconds.

A) Iw a/2t 2 B) Iw a2/tC) Iw a2/2t D) Iw a2/t 2E) Iw a2/2t 2

What is the average power delivered to the objectduring this interval t?

A) 3I B) 6I C) 9I D) 12I E) 15I

102. An object with a rotational inertia of I has anangular position (t) = 3t2 + 3t + 3, where is inradians and t is in seconds. What is the net torqueacting on the object?

A) 1:2 B) 1: C) 1:1 D) :1 E) 2:1

103. A ball rolls down an incline plane without slipping.What is the ratio of its angular velocity at h/3 to itsangular velocity at 2h/3?

A) Zero B) –0.5 JC) –0.2 J D) 0.2 JE) 0.5 J

104. A force on a circular object creates a torque thatvaries according to the equation t = cos , where isin N-m and is in degrees. How much work isdone by that force as the object rotates from 37° to53°?

A) Zero B) 3 J C) 3 J D) 6 J E) 6 J

105. How much work is done by a 15 N tangential forceon a disk of radius .2 m during one revolution?

A) 1:4 B) 1:2 C) 3:4 D) 2:1 E) 4:1

106. What is the ratio of translational kinetic energy torotational kinetic energy for a solid cylinder rollingat a constant speed v along a flat surface?

A) 1:5 B) 2:5 C) 1:2 D) 2:1 E) 5:2

107. What is the ratio of translational kinetic energy torotational kinetic energy for a solid sphere rollingat a constant speed v along a flat surface?

A) 1 kgm2 B) 2 kgm2

C) 4 kgm2 D) 8 kgm2

E) 20 kgm2

108. What is the moment of inertia of a spinning objectof radius 0.5 m and mass 6 kg moving at 5 m/s, if ithas a kinetic energy of 100 J?

A) Zero B) 2 m/sC) 4 m/s D) 6 m/sE) 10 m/s

109. A solid sphere of radius 0.2 m and mass 2 kg is atrest at a height 7 m at the top of an inclined planemaking an angle 60° with the horizontal.Assuming no slipping, what is the speed of thecylinder at the bottom of the incline?

A) It is perpendicular to both the radius vectorand the linear momentum vector.

B) It is in the same direction as the radius vector.C) It is in the same direction as the linear

momentum vector.D) It is in the same plane as both the radius

vector and the linear momentum vector.E) Angular momentum is not a vector quantity.

110. Which of the following is true of the angularmomentum vector?

A) Mv B) Mv/rC) Mrv/2 D) MrvE) 2Mrv

111. A cylinder of mass M and radius r rolls with alinear velocity v. What is its angular momentum?

A) 0.5 kg B) 1 kgC) 2 kg D) 4 kgE) 5 kg

112. What is the mass of a hoop that a radius of 2.5 mand has an angular momentum of 25 kg•m2 when itrolls with at a speed of 10 m/s?

A) 2 m B) 3 m C) 4 m D) 6 m E) 9 m

113. If a wheel of moment of inertia 24 kg•m2 moves ata velocity of 6 m/s and has an angular momentumof 36 kg•m2/s, what is its radius?

A) 1:1 B) 1:2 C) 2:5 D) 2:1 E) 5:4

114. If a cylinder and a hoop of the same mass and sameradius both roll with the same angular velocity,what is the ratio of the angular momentum of thecylinder to the angular momentum of the hoop?

A) 1:1 B) 2:5 C) 4:5 D) 5:4 E) 5:2

115. A sphere and a cylinder of equal mass and equalradius are rolling with equal angular momentum. What is the ratio of the angular speed of the sphereto the angular speed of the cylinder?

A) 48 kg•m2/s B) 96 kg•m2/sC) 120 kg•m2/s D) 144 kg•m2/sE) 240 kg•m2/s

116. What is the angular momentum of a sphere withradius 2 m and mass 5 kg that rotates at a speed of12 rad/s?


117. What is the angular velocity of a cylinder ofradius 2 m and mass 6 kg that has an angularmomentum of 24 kg•m2/s?


118. What is the angular velocity of a hoop of radius 1m and mass 3 kg that has an angular momentum of18 kg•m2/s?

A) 5 kg•m2/s? B) 10 kg•m2/s?C) 20 kg•m2/s? D) 25 kg•m2/s?E) 30 kg•m2/s?

119. What is the angular momentum of a hoop withradius 1 m and mass 5 kg that moves with angularvelocity 4 rad/s?

A) 10 kg•m2/s B) 10 kg•m3/sC) 20 kg•m2/s D) 20 kg•m3/sE) 40 kg•m2/s

120. What is the angular momentum of a wheel withrotational inertia 5 kg•m2 and angular velocity 4rad/s?

A) the product of rotational inertia and angularvelocity

B) the product of moment of inertia and angularvelocity

C) angular momentumD) kinetic energyE) the derivative of rotational kinetic energy with

respect to angular velocity

121. The cross product of radius and linear momentumis equivalent to all of the following EXCEPT

A) 0.1 m B) 0.2 mC) 0.3 m D) 0.4 mE) 0.5 m

122. A unicycle travels at 6.0 m/s. Its wheel has anangular momentum of 300 kgm2/s and a momentof inertia of 10 kgm2. What is its radius?

A) 15 kgm2/s B) 27 kgm2/sC) 30 kgm2/s D) 54 kgm2/sE) 60 kgm2/s

123. The angular position of a sphere is given by theequation (t) = 2t2 + 3t + 6, where is in radiansand t is in seconds. If the moment of inertia for thesphere is 4 kgm2, then what is its angularmomentum at t = 3 s?


124. A unicycle travels at 5.0 m/s. Its wheel has a radiusof .4 m and a moment of inertia of 20 kgm2. Whatis its angular momentum?

A) 2:5 B) 4:5 C) 1:1 D) 5:4 E) 5:2

125. What is the ratio of angular momentum for a solidsphere and a solid cylinder with the same angularvelocities, masses and radii?

A) 0.1 kg B) 1 kgC) 2 kg D) 5 kgE) 10 kg

126. A solid cylinder with diameter 20 cm has anangular velocity of 10 m/s and angular momentumof 2 kgm2/s. What is its mass?

A) 1 gm2/s B) 3 gm2/sC) 6 gm2/s D) 9 gm2/sE) 10 gm2/s

127. A slender rod with mass .6 kg and length 10 cm hasan angular velocity of 2 m/s. The moment ofinertia for a slender rod is calculated by ML 2.What is its angular momentum?


128. A uniform sphere has a moment of inertia 2 kgm2

and an angular velocity or 5 m/s. What is itsangular momentum?

A) Radius and forceB) Radius and linear momentumC) Radius and rotational velocityD) Force and rotational velocityE) Torque and rotational velocity

129. Angular momentum can be calculated by taking thecross product of

A) 2 N•s B) 6 N•m/kgC) 12 kg•m/s D) 24 m2/sE) 64 kg•m2/s

130. A 4 kg object moves in a circle of radius 8 m at aconstant speed of 2 m/s. What is the angularmomentum of the object with respect to an axisperpendicular to the circle and through its center?

A) 6 m B) 8 m C) 12 m D) 16 m E) 18 m

131. A 3 N force is exerted on an infinitely large wheelof moment of inertia 12 kg•m2. At what distancefrom the center of the wheel should the force beexerted in order for the wheel to accelerate with aangular acceleration of 2 rad/s2, assuming the forceis exerted perpendicular to the radius of the wheelin the plane of the wheel?

Base your answers to questions 132 and 133 on thediagram below.

A) mg/I B) (mgh/2I)C) (mgh/I) D) (2mgh/I)E) 2mg/I

132. The rod of rotational inertia I is initially at rest. Aball of mass m falls onto the rod such that all of itskinetic energy is imparted to the rod. What is therotational velocity of the rod around point P immediately after the collision?

A) It will increase.B) It will remain the same.C) It will decrease.D) The effect depends where the mass is attached

to the system.E) The effect depends on the ratio of m to the

mass of the rod.

133. If the mass m is attached to the moving systemwithout imparting a force on the system, what isthe effect on the total angular momentum of thesystem?

A) w /4 B) w /2 C) w D) 2w E) 4w

134. If an object is initially spinning at an angularvelocity of w, what is its new angular velocity if itsrotational inertia increases by a factor of 2?

A) w /16 B) w /4C) 2w D) 4wE) 16w

135. If an object is initially spinning at an angularvelocity of w, what is its new angular velocity if itsrotational inertia decreases by a factor of 4?

Base your answers to questions 136 and 137 on theinformation below.

A figure skater of moment of inertia 40 kg•m2 isinitially spinning at a speed of 6 rad/s. If she movesher arms outward, her new moment of inertia is 60kg•m2.

A) 120 J B) 180 J C) 240 J D) 360 J E) 480 J

136. How much work does the skater do in order tomove her hands outward to this position?


137. What is her new angular velocity?

A) it will be halvedB) it will remain the sameC) it will be doubledD) it will decrease by a factor of fourE) it will increase by a factor of four

138. Assuming no torque acts on the object, what willhappen to the angular velocity if its moment ofinertia is halved?

A) her rotational inertiaB) her angular velocityC) her linear speedD) her angular displacementE) her angular momentum

139. A figure skater in the middle of a spin moves herarms farther from her body. Which of thefollowing will remain the same?

A) v 0/4 B) v 0/2 C) v 0 D) 2v 0 E) 4v 0

140. An object spins with velocity v 0. Its radius ishalved and its inertia is doubled. What is its newvelocity?

A) I0/4 B) I0/2 C) I0 D) 2I0 E) 4I0

141. An spinning object has moment of inertia I0. Whatis its inertia if its radius is halved but itstranslational velocity stays the same?

A) v 0/4 B) v 0/2 C) v 0 D) 2v 0 E) 4v 0

142. An object is spinning with an initial velocity of v 0.What is its final velocity if its radius is halved butits inertia stays the same?

A) translational velocityB) linear momentumC) torqueD) inertiaE) angular velocity

143. Which of the following is equal to the timerate-of-change of angular momentum?

A) w /4 B) w /2 C) w D) 2w E) 4w

144. An object spins with angular velocity w. If theobject’s moment of inertia increases by a factor of4 with no added torque what is the object’s newangular velocity?

A) w M/2(m+M) B) w M/(m+M)C) w M/2M D) w M/2mE) 2w M/(m+M)

145. A solid disk of mass M and radius R is spinningwith an angular velocity of w when a disk of thesame radius but mass m is placed on top. What isthe new angular velocity in terms of M, R and w?

A) w 0/9 B) w 0/3 C) w 0 D) 3w 0 E) 9w 0

146. A figure skater spins with an angular velocity of w 0 on the ice holding his arms out perpendicular tohis body. He then brings his arm in towards hisbody causing his rotational inertia to decrease by afactor of 3. What is his new angular velocity?

A) 75 kg B) 94 kgC) 150 kg D) 300 kgE) 350 kg

147. A person with a mass of 75 kg goes to a planet withtwice the radius and half the mass of earth. What istheir mass on this planet?

A) 87.5 N B) 93.75 NC) 187.5 N D) 250.25 NE) 1500 N

148. A person with a mass of 75 kg goes to a planet withtwice the radius and half the mass of earth. What istheir weight on this planet?

A) the force of gravity is halvedB) the force of gravity is doubledC) the force of gravity is unchangedD) the force of gravity is quadrupledE) the force of gravity is increased by a factor of

8

149. If the distance between the center of gravity of asatellite and the center of gravity of the Earth ishalved and the mass of the satellite is doubled, then

A) their mass has decreased by a factor of 2B) their mass has been reduced by a factor 4C) their weight has been reduced by a factor of 2D) their weight has been reduced by a factor of 4E) their mass and weight are both reduced by a

factor of 2

150. A space ship fires a weapon at a planet, destroyinghalf its mass. The planet's inhabitants would findthat

A) 16:1 B) 4:1 C) 1:1 D) 1:4 E) 1:16

151. Object A has mass m and is on the surface of theEarth (radius = R). Object B also has mass m, but isa distance 4R from the Earth's center. The ratio ofthe weight of A to B is

A) 4W B) 2W C) W D) E)

152. An object has a weight W when it is on the surfaceof the Earth (radius = R). When the same object is adistance 2R from the center of the Earth, its weightwill be

A) F B) F C) F D) F E) 6F

153. Gravitational force F exists between point objects A and B separated by distance R. If the mass of A isdoubled and distance R is tripled, what is the newgravitational force between A and B?

A) F B) F C) 3F D) 9F E) 81F

154. Two objects, each of mass M, are a distance R apart. The gravitational force between them is F. If the mass of each object were tripled, thegravitational force between the objects would be

A) B)

C) D)

E)

155. An object with mass m above the surface of theEarth (mass = M) is dropped from an altitude equalto the Earth's radius (R). At what speed will theobject impact the Earth?

A) 100 N B) 200 NC) 400 N D) 800 NE) 1600 N

156. An object is on the surface of a planet that has halfthe mass and half the radius of the Earth. If theobject weighs 400 N on Earth, on this planet it willweigh

A) 10 kg B) 20 kgC) 40 kg D) 80 kgE) 160 kg

157. An object is on the surface of a planet that hastwice the mass and twice the radius of the Earth. Ifthe object has a mass of 40 kg on Earth, its mass onthis planet will be

A) Rv G

B) Rv2 2GC) Rv2 GD) 2Rv2 GE) G

Rv2

158. A planet has a radius R. An object is dropped froma distance 2R from the planet's center, and reachesa speed of v just before hitting the surface. Themass of the planet is

A) B) C) D) E)

159. In the diagram above, two masses, one of mass m,the other of mass 9m, are a distance r apart. Alongthe line shown, at which distance from the mass m will the gravitational force on an object be least?

A) 2 m/s2 B) 4 m/s2C) 8 m/s2 D) 10 m/s2E) 15 m/s2

160. A certain planet Earth Prime has a mass 10 timesthat the of the Earth, and 5 times the radius of theEarth. The value of g on Earth Prime is most nearly

A) 4w B) 0 C) D) E)

161. An object on the surface of the earth has a weight w. If the object is brought to an altitude that is 2times the radius of the Earth, its weight will be

A) 100:1 B) 10:1C) 1:1 D) 1:10E) 1:100

162. A moon with mass m is orbiting a planet with amass of 10m. The ratio of the force the planetexerts on the moon to the force the moon exerts onthe planet is

A) B) C) F D) 3F E) 9F

163. Two experiments are conducted. In Experiment A,two objects with mass m are at a distance r apart.In Experiment B, two objects with mass 3m are adistance 3r apart. If the gravitational force betweenthe two masses in A is F, what will be the forcebetween the objects in B?

A) be doubled.B) be halved.C) decrease by a factor of 4.D) increase by a factor of 4.E) remain the same.

164. Two masses are placed a distance apart, and exert agravitational force upon each other. If one of themasses is doubled, the gravitational force betweenthe masses will

A) B) C) 2F D) 4F E) F 2

165. Two point particles have a gravitational forcebetween them with a magnitude of F. The distancebetween them is halved. The gravitational forcebetween these two particles will now be

A) 2.1 m/s2 B) 9.8 m/s2C) 26 m/s2 D) 87 m/s2E) 360 m/s2

166. A planet has a mass 320 times that of the Earth anda radius 11 times that of the Earth. What is theacceleration due to gravity at the surface of thisplanet?

A) The centripetal force on the astronaut is zero.B) The gravitational pull of the sun cancels out

the gravitational pull from the earth.C) The spaceship is in freefall.D) The force of gravity decreases as the astronaut

travels further away from the earth.E) The spaceship is traveling with a constant

velocity.

167. Which of the following statements explains whyastronauts feel weightless while orbiting the earth?

A) 1 N B) 2 N C) 4 N D) 10 N E) 20 N

168. An object weighs 10 N on the earth's surface.What is the weight of the object on a planet whichhas one tenth the earth's mass and one half theearth's radius?

A) mgB) 2mgC) 4mgD) mg

2E) mg

4

169. A satellite of mass m orbits the earth at a height 2times the radius of the earth from the earth's center.If mg is the weight of the satellite on earth, what isits weight at its current location?

A) F B) F C) 3F D) 9F E) 10F

170. Two masses, m and M are a distance L away fromeach other. They cause a gravitational force F onone another. If the masses are then moved to adistance 3L away from each other, what does theforce become?

A) 80 N B) 90 NC) 180 N D) 270 NE) 540 N

171. Planet X has 3 times the mass of earth and twice thediameter. If an object weighs 120 Newtons onEarth, how much would it weigh on planet X?

A) 8.8 m/s2 B) 11.4 m/s2C) 35 m/s D) 123 m/sE) 490 m/s

172. Uranus has a mass 14 times that of Earth and adiameter 4 times that of Earth. The acceleration ofa falling body near the surface of Uranus is mostnearly

A) g B) g C) g D) g E) 2g

173. Planet A has twice the radius of planet B and onehalf of the mass. If the acceleration of an object infree fall on planet B is g, what is the acceleration ofan object in free fall on planet A?

A) B) C) 1 D) 2 E) 4

174. Two spheres, A and B, of equal density are placed adistance of d apart. Sphere A has twice volume ofsphere B, and the spheres are subject only to theirmutual gravitational pull.

What is the ratio of the acceleration of sphere A tothe acceleration of sphere B?

A) 300 NB) 800 N

C) 600 ND) 600 NE) 1200 N

175. A person weighing 600 N on earth travels to aplanet with 4 times the mass and twice the radius ofEarth. The person's weight on this planet is mostnearly

A) I only B) III onlyC) I and III only D) II and III onlyE) I, II, and III

176. Two planets have the same mass, but differentradii, and no atmospheres. Which of the followingwould be the same for objects of equal mass andsize on the surfaces of the two planets?

I. The rate of free fall.II. The upward buoyancy force felt by each whenplaced in water.III. The amount of momentum each would acquirewhen given a certain impulse.

A) I only B) II onlyC) I and II only D) II and III onlyE) I, II, and III

177. Two planets have the same size but differentmasses and no atmospheres. Which of thefollowing would be the same for objects of equalmass on the surfaces of the two planets?

I. The rate at which each would fall freely.II. The amount of force needed to cause a givenhorizontal acceleration.III. The amount that each of them would stretch aspring that was held vertically.

A) 0.5 s B) 1.0 s C) 1.4 s D) 2.0 s E) 2.8 s

178. A simple pendulum has a period of approximately2.0 s on earth. What is its period on an imaginaryplanet the same size as earth, but half the mass ofearth?

A) GMm 2r

B) GMm 4r

C) GMm r

D) GMm r 2

E) GMm 4r 2

179. The Moon, mass m, orbits the Earth, mass M, in acircular orbit with radius r. What is the kineticenergy of the Moon in its orbit?

A) I only B) III onlyC) I and III, only D) II and III, onlyE) I, II, and III

180. A satellite moves in a circular orbit around a planetat a constant speed. Which of the following mustbe true?

I. The net force on the satellite is always radiallyinward.II. The net work done on the satellite in the intervalof half an orbit zero.III. The angular momentum of the satellite isconstant.

Base your answers to questions 181 and 182 on thefollowing.

An astronomical unit (AU) is defined as the meandistance at which the Earth orbits the Sun.

A) 5 AU B) 9 AUC) 18 AU D) 27 AUE) 44 AU

181. The planet Krypton orbits a star 2 times moremassive than the Sun. It takes 27 Earth years tocircle this star. The radius of Krypton's orbit ismost nearly

A) 3 Earth years. B) 6 Earth years.C) 15 Earth years. D) 39 Earth years.E) 216 Earth years.

182. If the planet P orbits at a mean distance of 6 AU, ayear on P is most nearly

A) B)

C) D)

E)

183. A moon orbits a planet in a circular orbit of radius R. If the mass of the planet is M, what is the periodof the moon's revolution?

A) be doubled.B) be halved.C) decrease by a factor of 4.D) increase by a factor of 4.E) remain the same.

184. If the radius of a satellite's orbit is doubled, it'skinetic energy will

A) B) C) D) E)

185. A satellite orbits the Earth in at a distance of 1Earth radius from the surface. Its velocity is v. Ifthe satellite moves and enters a new orbit at 3 Earthradii from the Earth's surface, its new velocity willbe

A) 0.004 hr B) hrC) 3 hr D) 9 hrE) 27 hr

186. A satellite in orbit around the Earth has a period ofone hour. An identical satellite is placed in an orbithaving a radius which is nine times larger than thefirst satellite. What is the period of the secondsatellite?

A) The satellite is in dynamic equilibrium.B) The acceleration on the satellite is zero.C) The centripetal force is in the direction of the

velocity of the satellite.D) The centripetal force is equivalent to the

reaction force caused from the satellite.E) The centripetal force is perpendicular to the

velocity of the satellite.

187. The Earth exerts the necessary centripetal force onan orbiting satellite to keep it moving in a circle atconstant speed. Which of the following statementsbest explains why the speed of the satellite does notchange even though there is a net force exerted onit?

A) B) C) D) E)

188. A satellite is orbiting around the Earth at a radius of2R from its center. What is the magnitude of thevelocity it is traveling at?

A) Mass: MRadius: R

B) Mass: MRadius: R

C) Mass: MRadius: R

D) Mass: 2MRadius: R

E) Mass: MRadius: 2R

189. Five planets make circular orbits around a starwhich is much more massive than any of them.The mass and orbital radius of each satellite isgiven. Which satellite has the longest period?

A) circular B) parabolicC) elliptical D) hyperbolicE) spherical

190. A planet orbits around a star which is not at thecenter of its orbit. The shape of the orbit is mostlikely

A) –GMm/2a B) –GMm/aC) GMm/4a D) GMm/2aE) GMm/a

191. What is the total energy of a satellite of mass m thatorbits a planet of mass M in an elliptical orbit withsemi-major axis a?

A) Kepler's First LawB) Kepler's Second LawC) Kepler's Third LawD) Conservation of angular momentumE) None of the above

192. The planets orbit in elliptical paths with the sun atone focus of the ellipse. This statement is bestknown as


193. Planets sweep out equal areas in equal times. Thisstatement is best known as


194. The square of the period of an orbit is proportionalto the cube of the semimajor axis of the orbit. Thisstatement is best known as

Base your answers to questions 195 and 196 on thepicture below, which represents a planet that movesin an elliptical orbit with a star as one focus as shownabove.

A) A and E B) A and DC) B and C D) B and EE) C and D

195. At which two points does the planet have the samevelocity?


196. At which point does the planet have the greatestpotential energy?

Answer Keyrotation review 13

1. B2. A3. E4. C5. D6. E7. E8. E9. D10. D11. D12. C13. E14. B15. C16. C17. B18. C19. B20. B21. B22. C23. A24. C25. D26. D27. B28. C29. D30. A31. A32. B33. A34. A35. E36. D

37. B38. E39. D40. D41. C42. B43. C44. A45. B46. D47. C48. D49. D50. D51. B52. B53. C54. A55. C56. B57. A58. D59. C60. B61. B62. C63. E64. D65. D66. A67. C68. A69. E70. B71. A72. C

73. B74. E75. B76. D77. E78. E79. B80. C81. B82. C83. E84. B85. C86. D87. C88. A89. C90. C91. B92. B93. C94. D95. E96. C97. A98. A99. C100. E101. C102. B103. D104. D105. E106. D107. E108. B

109. E110. A111. C112. B113. C114. B115. D116. B117. B118. B119. C120. C121. D122. B123. E124. E125. B126. E127. A128. A129. B130. E131. B132. D133. B134. B135. D136. C137. B138. C139. E140. E141. B142. D143. C144. A

Answer Keyrotation review 13

145. B146. D147. A148. B149. E150. C151. A152. E153. A154. D155. C156. D157. C158. B159. C160. B161. E162. C163. C164. A165. D166. C167. C168. C169. E170. B171. B172. A173. A174. B175. C176. B177. B178. E179. C180. E

181. B182. C183. D184. B185. D186. E187. E188. A189. E190. C191. A192. A193. B194. C195. D196. D

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