Circular Motion Name _________________________

1. In the game of tetherball, the struck ball whirls around a pole. In what direction does the net force on the ball point?

a. Toward the top of the poleb. Toward the groundc. Along the horizontal component of the tension forced. Along the vertical component of the tension forcee. Tangential to the circle

2. You are a passenger in a car, not wearing a seat belt. The car makes a sharp left turn. From your perspective in the car, what do you feel is happening to you?

a. You are thrown to the rightb. You feel no particular changec. You are thrown to the leftd. You are thrown to the ceilinge. You are thrown to the floor

3. During that sharp left turn, you found yourself hitting the passenger door. What is the correct description of what is actually happening?

a. Centrifugal force is pushing you into the doorb. The door is exerting a leftward force on youc. Both of the aboved. Neither of the above

4. You drive your dad’s car too fast around a curve and the car starts to skid. What is the correct description of this situation?

a. Car’s engine is not strong enough to keep the car from being pushed outb. Friction between tires and road is not strong enough to keep car in a circlec. Car is too heavy to make the turnd. A deer caused you to skide. None of the above

5. A ping pong ball is shot into a circular tube that is lying flat (horizontal) on a tabletop. When the ping pong ball leaves the track, which path will it follow?

6. Two equal mass rocks tied to strings are whirled in horizontal circles. The radius of circle 2 is twice that of circle 1. If the period of motion is the same for both rocks, what is the tension in cord 2 compared to cord 1?

a. T2 = ¼ T1 b. T2 = ½ T1 c. T2 = T1 d. T2 = 2T1 e. T2 = 4T1

12

3

4 5

7. A rider in a “barrel of fun” finds herself stuck with her back to the wall. Which diagram correctly shows the forces acting on her?

8. You’re on a Ferris wheel moving in a vertical circle. When the Ferris wheel is at rest, the normal force N exerted by your seat is equal to your weight mg. How does N change at the top of the Ferris wheel when you are in motion?

a. N remains equal to mgb. N is smaller than mgc. N is larger than mgd. None of the above

9. A skier goes over a small round hill with radius R. Since she is in circular motion, there has to be a centripetal force. At the top of the hill, what is Fc of the skier equal to?

a. Fc = N + mgb. Fc = mg - Nc. Fc = T + N - mgd. Fc = Ne. Fc = mg

1 2 3 4 5

10. You swing a ball at the end of string in a vertical circle. Since the ball is in circular motion there has to be a centripetal force. At the top of the ball’s path, what is Fc equal to?

a. Fc = T - mgb. Fc = T + N - mgc. Fc = T + mgd. Fc = Te. Fc = mg

11. Which is stronger, Earth’s pull on the Moon, or the Moon’s pull on Earth?a. The Earth pulls harder on the Moonb. The Moon pulls harder on the Earthc. They pull on each other equallyd. There is no force between the earth and the Moone. It depends upon where the Moon is in its orbit at that time

12. If the distance to the Moon were doubled, then the force of attraction between Earth and the Moon would be :

a. One quarter b. one half c. the same d. two times e. four times

13. You weigh yourself on a scale inside an airplane that is flying with constant speed at an altitude of 20,000 ft. How does your measured weight in the airplane compare with your weight as measured on the surface of the Earth?

a. Greater than b. less than c. same

14. Two satellites A and B of the same mass are going around Earth in concentric orbits. The distance of satellite B from Earth’s center is twice that of satellite A. What is the ratio of the centripetal force acting on B compared to that acting on A?

a. 1/8 b. ¼ c. ½ d. it’s the same e. 2

15. The Moon does not crash into Earth because:a. It’s in Earth’s gravitational fieldb. The net force on it is zeroc. It is beyond the main pull of Earth’s gravityd. It’s being pulled by the sun as well as by Earthe. None of the above

16. Astronauts in the space shuttle float because:a. They are so far from Earth that Earth’s gravity doesn’t act any more.b. Gravity’s force pulling them inward is cancelled by the centripetal force pushing them

outward.c. While gravity is trying to pull them inward, they are trying to continue on a straight line

path.d. Their weight is reduced in space so the force of gravity is much weaker

17. If you weigh yourself at the equator of Earth, would you get a bigger, smaller, or similar value than if you weigh yourself at one of the poles?

a. Bigger b. smaller c. same

18. A planet of mass m is a distance d from Earth. Another planet of mass 2m is a distance 2d from Earth. Which force vector best represents the direction of the total gravitation force on Earth?

5

4

321

2d

d

m

2m

19. Which of the following must be true of an object in uniform circular motion?a. Its velocity must be constantb. Its acceleration and its velocity must be in opposite directionsc. Its acceleration and its velocity must be perpendicular to each other.d. It must experience a force away from the center of the circle.e. Its acceleration must be negative.

20. A ball of mass m on a string swings back and forth to a maximum angle of 30 degrees to the vertical. Which of the following vectors represents the acceleration, a, of the mass at point A, the highest point in the swing?

a. b. c. d. a = zero e.

21. A planet of mass m orbits in a circle around a sun. The speed of the planet in its orbit is v; the distance from the planet to the sun is d. What is the magnitude and direction of the net force experienced by the planet?

a. v2

d, toward the sun

b. m v2

d, toward the sun

c. m v2

d, away from the sun

d. m v2

d, along the orbital path

A

B

e. v2

d, along the orbital path

22. A satellite orbits the moon in a circle of radius R. If the satellite must double its speed but maintain a circular orbit, what must the new radius of its orbit be?

a. 2R b. 4R c. ½ R d. ¼ R e. R

22. The Space Shuttle orbits 300 km above the Earth’s surface; the Earth’s radius is 6400 km. What is the gravitational acceleration experienced by the Space Shuttle?

a. 4.9 m/s2 b. 8.9 m/s2 c. 9.8 m/s2 d. 10.8 m/s2 e. zero

23. What is the speed of a moon with a period of 20 hours that is orbiting a planet of radius R at a distance 5 R from the planet’s center?

a.26000πR

m /s b. πR26000

m /s c. R

36000πm /s

d. πR7200

m /s e. π2R720

m/ s

24. What is the period of an object in uniform circular motion with a radius of 25 cm with a centripetal acceleration of 35 m/s2?

a. 0.53 s b. 3.1 s c. 6.6 s d. 12 s e. 33 s

25. In which of the following situations can the velocity and acceleration vectors be perpendicular?I. An object falling verticallyII. An object in uniform circular motionIII. An object in projectile motion

a. I only b. II only c. III only d. I and II only e. II and III only

26. What is the centripetal acceleration of an object in uniform circular motion at the end of a 1 meter rope making 1 revolution per second?

a. 39 m/s/s tangentially b. 39 m/s/s inward c. 39 m/s/s outward

d. 1 m/s/s inward e. 1 m/s/s tangentially

27. In an ideal situation, the force required to keep a 20 gram sphere turning at 15 revolutions per second at the end of a 35 cm string of negligible mass is

a. 17 N b. 45 N c. 62 N d. 121 N e. 515 N

28. What is the attractive force between the Earth and an 85 kg piece of debris in an orbit of radius 27,500 km with two revolutions per day?

a. 1.1 N b. 5.2 N c. 17 N d. 45 N e. 121 N

29. At what distance will two 1000 kg masses have the same attractive force for each other as gravity at the surface of the Earth would have on either one of them?

a. 1.1 × 100 m b. 9.8 × 10-1 m c. 2.9 × 10-3 m d. 8.3 × 10-5 m e. 4.5 × 10-7 m

30. What would be the value of the acceleration of gravity near the surface of the Earth if the Earth had the same mass and a radius of 6.6 × 106 m?

a. 9.16 m/s2 b. 9.31 m/s2 c. 9.77 m/s2 d. 9.9 m/s2 e. 10.3 m/s2

31. What is the period of a 1500 kg satellite in a circular orbit 48,000 km from the center of the Earth?

a. 24 hours b. 26 hours c. 29 hours d. 34 hours e. 51 hours

32. What is the frequency of a planet around a star in orbit at a mean distance of R, if it is twice the mean distance of a planet orbiting the same star with a frequency of 2.10 × 10 -5 rev/s?

a. 1.4 × 10-5 rev/s b. 7.4 × 10-6 rev/s c. 1.7 × 10-7 rev/s d. 6.8 × 10-7 rev/s

e. 2.4 × 10-8 rev/s

33. On a curved roadway of radius 100 m, the suggested speed limit is 25 mph (approximately 10 m/s). What must the coefficient of friction be between a car’s tires and the road for the car to safely negotiate the curve at the posted speed?

a. 0.1 b. 0.2 c. 0.3 d. 0.4 e. 0.5

34. An amusement park ride has a diameter of 16 meters and revolves at 15 rpm. How fast is a rider moving if she sits at the outermost part of the ride?

a. 29.4 m/s b. 1.07 m/s c. 225 m/s d. 12.56 m/s e. 9.8 m/s

35. What is the gravitational force between two runners standing 100 m apart on a track if their masses are 60 kg and 75 kg respectively?

a. 588 N for the first runner and 735 N for the second runner

b. 45 N c. 3 × 10-7 N d. 3 × 10-11 N e. 3 N

36. Which force in the diagram will produce the largest torque about the pivot shown?

a. 10 N b. 20 N c. 30 N d. 20 N e. 5 N

37. In the picture below, where should a third mass (6 kg) be hung to produce rotational equilibrium?

a. two meters to the right of the fulcrum

b. 1.88 meters to the left of the fulcrum

c. 1.5 meters to the right of the fulcrum

d. 0.17 meters to the left of the fulcrum

e. there is no place to put the mass so that it will balance

10 N 20 N 30 N 20 N 5 N

0 3 6 8

38. All of the following are true about torque except:

a. Its units are Newton meters

b. It can only be produced by a force.

c. Torque is zero unless the force has a component perpendicular to the moment arm.

d. A force whose line of action passes through the axis of rotation produces zero torque.

e. Torque may be clockwise or counterclockwise, depending on the direction the force points.

39. How much work is done by the centripetal force (in this case, the friction between the tires and the road) on a 1200 kg car moving on a circular track of radius 50 meters at a constant speed of 31.4 m/s?

a. 7.4 × 106 J b. 19.7 J c. 2136.7 J d. 117,600 J e. 0 J

40. A mass is moving in uniform circular motion under the effects of a centripetal force. If the force is doubled and the radius is cut in half, by what factor will the speed change?

a. It will double b. It will be cut in half c. It will not change

d. It will quadruple e. It will be √2 times faster

41. A circular, rotating space station uses centripetal force to produce artificial gravity. If the radius of the space station is 450 m and it spins at a speed of 55 m/s, what is the apparent value of g on the surface of the station?

a. 1.8 m/s2 b. 9.8 m/s2 c. 13.1 m/s2 d. 6.7 m/s2

e. zero, because in space everything is weightless

42. On an unknown planet, a pendulum of length 1.5 m swings with a period of 3.3 s. What is the acceleration due to gravity on this planet?

a. 3.7 m/s2 b. 12.7 m/s2 c. 7.1 m/s2 d. 5.4 m/s2 e. 9.8 m/s2

43. A 1.0 m long pendulum on a distant planet swings in simple harmonic motion with a period of 3 seconds. What is the approximate magnitude of the acceleration of gravity at this location?

a. 0 m/s2 b. 2 m/s2 c. 4 m/s2 d. 8 m/s2 e. 16 m/s2

44. An object traveling in a circle at constant speed:

a. has a constant velocity

b. is not in accelerated motion

c. has an inward, radial acceleration

d. has an outward, radial acceleration

e. has a constant tangential acceleration

45. The radius of the path of an object in uniform circular motion is doubled. For its speed to remain the same, the centripetal force on the object must be:

a. one fourth as much as before

b. half as great as before

c. the same as before

d. twice as great as before

e. four times as great as before

46. The moon’s mass is about one sixth of the earth’s mass. Compared to the gravitational force the earth exerts on the moon, the gravitational force the moon exerts on the earth:

a. is one sixth as much

b. is one half as much

c. is the same

d. is twice as much

e. is six times as much

47. A car is traveling at 10 m/s on a road such that the coefficient of friction between its tires and the road is 0.5. The minimum turning radius of the car is:

a. 5 m b. 10 m c. 20 m d. 40 m e. 50 m

48. Consider two satellites in circular orbits around the Earth but at different distances from the Earth.

a. Both experience the same centripetal acceleration.

b. The object nearer to Earth experiences the greater centripetal acceleration.

c. The object farther from Earth experiences the greater centripetal acceleration.

d. It depends upon the masses of the satellites, which are not known.

e. Neither has centripetal acceleration.

49. Which of the following would make an object of given mass, m, appear to increase in weight when compared to its weight when stationary on the surface of the earth?

I. object accelerating upward in an elevator

II. object in free fall

III. object in the Space Shuttle as it takes off from Earth’s surface

a. I only b. II only c. III only d. I and III e. I and II

50. A compact disc has a radius of 6 cm. If the disc rotates about its central axis at an angular speed of 5 rev/s, what is the linear speed of a point on the rim of the disc?

a. 0.3 m/s b. 1.9 m/s c. 7.4 m/s d. 52 m/s e. 83 m/s

51. A compact disc has a radius of 6 cm. If the disc rotates about its central axis at a constant angular speed of 5 rev/s, what is the total distance traveled by a point on the rim of the disc in 40 min?

a. 180 m b. 360 m c. 540 m d. 720 m e. 4.5 km

52. An object of mass 0.5 kg, moving in a circular path of radius 0.25 m, experiences a centripetal acceleration of constant magnitude 9 m/s2. What is the object’s angular speed?

a. 2.3 rad/s b. 4.5 rad/s c. 6 rad/s d. 12 rad/s e. can’t be determined

53. An object, originally at rest, begins spinning under uniform angular acceleration. In 10 s, it completes an angular displacement of 60 rad. What is the numerical value of the angular acceleration?

a. 0.3 rad/s2 b. 0.6 rad/s2 c. 1.2 rad/s2 d. 2.4 rad/s2 e. 3.6 rad/s2

54. In an effort to tighten a bolt, a force F is applied. If the distance from the end of the wrench to the center of the bolt is 20 cm and F = 20 N, what is the magnitude of the torque produced by F?

a. 0 Nm b. 1 Nm c. 2 Nm d. 4 Nm e. 10 Nm

55. What is the torque about a pendulum’s suspension point produced by the weight of the bob, given that the length of the pendulum, L, is 80 cm, m = 0.5 kg, and the angle is 60 degrees?

a. 0.5 Nm b. 1 Nm c. 1.7 Nm d. 2 Nm e. 3.4 Nm

56. A uniform meter stick of mass 1 kg is hanging from a thread attached at the stick’s midpoint. One block of mass m = 3 kg hangs from the left end of the stick, and another block, of unknown mass M, hangs below the 80 cm mark on the meter stick. If the stick remains at rest in the horizontal position, what is M?

a. 4 kg b. 5 kg c. 6 kg d. 8 kg e. 9 kg

57. What is the rotational inertia of the following body about the indicated rotation axis? The masses of the connecting rods are negligible.

Rotation axis

8/3 L

a. 4mL2 b. 32/3 mL2 c. 64/9 mL2 d. 128/9 mL2 e. 256/9 mL2

58. The moment of inertia of a solid uniform sphere of mass M and radius R is given by the equation I = 2/5 MR2. Such a sphere is released from rest at the top of an inclined plane of height h, length L, and incline angle θ. If the sphere rolls without slipping, find its speed at the bottom of the incline.

a. √ 107 gh b. √ 52 gh c. √ 72 gh d. √ 27 gLsinθ e. √ 710 gLsinθ

59. An object spins with angular velocity ω. If the object’s moment of inertia increases by a factor of 2 without the application of an external torque, what will be the object’s new angular velocity?

a. ω/4 b. ω/2 c. ω/√2 d. √2 ω e. 2 ω

60. If the distance between two point particles is doubled, then the gravitational force between them

a. decreases by a factor of 4

L L

b. decreases by a factor of 2

c. increases by a factor of 2

d. increases by a factor of 4

e. cannot be determined without knowing the masses