1. Two kinds of moving in circles
Rotary (rotational)= axis of motion at center of movement (sit and spin)
Circular motion=axis of rotation outside of object

2. Always use radians=r=57.3˚ 1 revolution=360 ˚ = 2 π radians
Angular quantities
Always use radians=r=57.3˚
1 revolution=360 ˚ = 2 π radians
Counterclockwise is +
Clockwise -

3. Holt book p247 #1 Θ(theta)= angular displacement in rad Θ =Δs/ r
s= arc length in meters. r= radius

4. ω = Θ/ Δ t Holt p 248 # 2 ω (lower case omega)=angular speed
measured in rad/s
Convert rev/s or rev/ min
ω = Θ/ Δ t

5. α ( lower case alpha)= angular acceleration Rad/s/s or rad/s2
Holt p 250 #2
α ( lower case alpha)= angular acceleration
Rad/s/s or rad/s2
α =Δ ω/ Δ t

6. Larger radius= greater vt uniform circular motion= speed is constant.
Section 1 Circular Motion
Chapter 7
tangential speed (vt) =speed along an imaginary line drawn tangent to the circular path.
Larger radius= greater vt
uniform circular motion= speed is constant.

7. Where Vt = tangential velocity (linear velocity)
Holt p255 #4
Vt= r ω
Where Vt = tangential velocity (linear velocity)
at=rα
Where at= tangential acceleration
(Linear acceleration)

8. Centripetal Acceleration
Section 1 Circular Motion
Chapter 7
Centripetal Acceleration

9. Centripetal Acceleration
Section 1 Circular Motion
Chapter 7
Centripetal Acceleration
centripetal acceleration= acceleration in a circular path at constant speed is due to a change in direction.

10. Section 1 Circular Motion
Chapter 7
(a.

11. Any type of force or combination of forces can provide this net force.
Section 1 Circular Motion
Chapter 7
Centripetal force =name given to the net force on an object in uniform circular motion.
Any type of force or combination of forces can provide this net force.
friction
gravitational force.
Tension

12. Section 1 Circular Motion
Chapter 7
Centripetal Force,
Centripetal force is always directed to the center of the circular path.

13. Section 1 Circular Motion
Chapter 7

14. Section 2 Newton’s Law of Universal Gravitation
Chapter 7
Objectives
Explain how Newton’s law of universal gravitation accounts for various phenomena, including satellite and planetary orbits, falling objects, and the tides.
Apply Newton’s law of universal gravitation to solve problems.

15. Gravitational Force, continued
Section 2 Newton’s Law of Universal Gravitation
Chapter 7
Gravitational Force, continued
The centripetal force that holds the planets in orbit is the same force that pulls an apple toward the ground—gravitational force.
Gravitational force is the mutual force of attraction between particles of matter.
Gravitational force depends on the masses and on the distance between them.

16. Gravitational Force, continued
Section 2 Newton’s Law of Universal Gravitation
Chapter 7
Gravitational Force, continued
The constant G, called the constant of universal gravitation, equals  10–11 N•m2/kg.

17. Gravitational Force, continued
Section 2 Newton’s Law of Universal Gravitation
Chapter 7
Gravitational Force, continued
The gravitational forces always equal and opposite.
Action reaction pair.

18. Newton’s Law of Universal Gravitation
Section 2 Newton’s Law of Universal Gravitation
Chapter 7
Newton’s Law of Universal Gravitation

19. Newton’s law of gravitation accounts for ocean tides.
Section 2 Newton’s Law of Universal Gravitation
Chapter 7
Newton’s law of gravitation accounts for ocean tides.
High and low tides are due to the gravitational force exerted on Earth by its moon and the sun.
Semi diurnal tidal pattern (two high and low tides)

21. Applying the Law of Gravitation, continued
Section 2 Newton’s Law of Universal Gravitation
Chapter 7
Applying the Law of Gravitation, continued
weight = mass  gravitational field strength
Because it depends on gravitational field strength, weight changes with location:
On the surface of any planet, the value of g, as well as your weight, will depend on the planet’s mass and radius.

22. Universal gravitation
What is the gravitational force between you and the earth given your mass of 70 kg and the earths mass of 5.98 X1024 kg and a radius of 6.38 X10 6 m?

23. Chapter 7 Objectives Describe Kepler’s laws of planetary motion.
Section 3 Motion in Space
Chapter 7
Objectives
Describe Kepler’s laws of planetary motion.
Relate Newton’s mathematical analysis of gravitational force to the elliptical planetary orbits proposed by Kepler.
Solve problems involving orbital speed and period.

24. Section 3 Motion in Space
Chapter 7
Kepler’s Laws
Kepler’s laws describe the motion of the planets.
First Law planets travel in elliptical orbits around the sun, the sun is at one of the focal points.

25. Chapter 7 Section 3 Motion in Space Keplers 2nd law the planet
travels faster when it
is closer to the sun
and slower when it is farther away.

26. Kepler’s third law states that T2  r3.
Section 3 Motion in Space
Chapter 7
Kepler’s third law states that T2  r3.
T= period of planet (time for 1 cycle or revolution.
The constant of proportionality is 4p2/Gm, where m is the mass of the object being orbited.
Thus

27. Kepler’s Laws, continued
Section 3 Motion in Space
Chapter 7
Kepler’s Laws, continued
Kepler’s third law the period of an object in a circular orbit depends on the same factors as speed of an object in a circular orbit :
Also Vt=2πr/T
hat m is the mass of the central object
The mean radius (r) =distance between the centers of the two bodies.

28. Section 3 Motion in Space
Chapter 7
Planetary Data

29. Chapter 7 Sample Problem Period and Speed of an Orbiting Object
Section 3 Motion in Space
Chapter 7
Sample Problem
Period and Speed of an Orbiting Object
Magellan was the first planetary spacecraft to be launched from a space shuttle. During the spacecraft’s fifth orbit around Venus, Magellan traveled at a mean altitude of 361km. If the orbit had been circular, what would Magellan’s period and speed have been?

30. Sample Problem, continued
Section 3 Motion in Space
Chapter 7
Sample Problem, continued
1. Define
Given:
r1 = 361 km = 3.61  105 m
Unknown:
T = ? vt = ?
2. Plan
Choose an equation or situation: Use the equations for the period and speed of an object in a circular orbit.

31. Sample Problem, continued
Section 3 Motion in Space
Chapter 7
Sample Problem, continued
Use Table 1 in the textbook to find the values for the radius (r2) and mass (m) of Venus.
r2 = 6.05  106 m m = 4.87  1024 kg
Find r by adding the distance between the spacecraft and Venus’s surface (r1) to Venus’s radius (r2).
r = r1 + r2
r = 3.61  105 m  106 m = 6.41  106 m

32. Sample Problem, continued
Section 3 Motion in Space
Chapter 7
Sample Problem, continued
3. Calculate
4. Evaluate
Magellan takes (5.66  103 s)(1 min/60 s)  94 min to complete one orbit.

33. Weight and Weightlessness
Section 3 Motion in Space
Chapter 7
Weight and Weightlessness
To learn about apparent weightlessness, imagine that you are in an elevator:
When the elevator is at rest, the magnitude of the normal force acting on you equals your weight.
If the elevator were to accelerate downward at 9.81 m/s2, you and the elevator would both be in free fall. You have the same weight, but there is no normal force acting on you.
This situation is called apparent weightlessness.
Astronauts in orbit experience apparent weightlessness.

34. Weight and Weightlessness
Section 3 Motion in Space
Chapter 7
Weight and Weightlessness

35. Chapter 7 Objectives Distinguish between torque and force.
Section 4 Torque and Simple Machines
Chapter 7
Objectives
Distinguish between torque and force.
Calculate the magnitude of a torque on an object.
Identify the six types of simple machines.
Calculate the mechanical advantage of a simple machine.

36. Chapter 7 Rotational Motion
Section 4 Torque and Simple Machines
Chapter 7
Rotational Motion
Rotational and translational motion can be analyzed separately.
For example, when a bowling ball strikes the pins, the pins may spin in the air as they fly backward.
These pins have both rotational and translational motion.
In this section, we will isolate rotational motion.
In particular, we will explore how to measure the ability of a force to rotate an object.

37. The Magnitude of a Torque
Section 4 Torque and Simple Machines
Chapter 7
The Magnitude of a Torque
Torque is a force to rotate an object around some axis.
How easily an object rotates depends on how much force is applied and on where the force is applied.
t = Fd sin q
torque = force  lever arm

38. The Magnitude of a Torque, continued
Section 4 Torque and Simple Machines
Chapter 7
The Magnitude of a Torque, continued
The applied force may act at an angle.
However, the direction of the lever arm (d sin q) is always perpendicular to the direction of the applied force, as shown here.

39. Section 4 Torque and Simple Machines
Chapter 7
Torque

40. Torque and the Lever Arm
Section 4 Torque and Simple Machines
Chapter 7
Torque and the Lever Arm
In each example, the cat is pushing on the door at the same distance from the axis. To produce the same torque, the cat must apply greater force for smaller angles.

41. Torque is a vector quantity. is (+)if the rotation is counterclockwise
Section 4 Torque and Simple Machines
Chapter 7
The Sign of a Torque
Torque is a vector quantity.
is (+)if the rotation is counterclockwise
and (-) if the rotation is clockwise.

42. Section 4 Torque and Simple Machines
Chapter 7
The Sign of a Torque

43. Chapter 7 Sample Problem Torque
Section 4 Torque and Simple Machines
Chapter 7
Sample Problem
Torque
A basketball is being pushed by two players during tip-off. One player exerts an upward force of 15 N at a perpendicular distance of 14 cm from the axis of rotation.The second player applies a downward force of 11 N at a distance of 7.0 cm from the axis of rotation. Find the net torque acting on the ball about its center of mass.

44. Sample Problem, continued
Section 4 Torque and Simple Machines
Chapter 7
Sample Problem, continued
1. Define
Given:
F1 = 15 N F2 = 11 N
d1 = 0.14 m d2 = m
Unknown:
tnet = ?
Diagram:

45. Sample Problem, continued
Section 4 Torque and Simple Machines
Chapter 7
Sample Problem, continued
2. Plan
Choose an equation or situation: Apply the definition of torque to each force,and add up the individual torques.
t = Fd
tnet = t1 + t2 = F1d1 + F2d2
Tip: The factor sin q is not included in the torque equation because each given distance is the perpendicular distance from the axis of rotation to a line drawn along the direction of the force. In other words, each given distance is the lever arm.

46. Sample Problem, continued
Section 4 Torque and Simple Machines
Chapter 7
Sample Problem, continued
Calculate
Substitute the values into the equation and solve: First,determine the torque produced by each force.Use the standard convention for signs.
t1 = F1d1 = (15 N)(–0.14 m) = –2.1 N•m
t2 = F2d2 = (–11 N)(0.070 m) = –0.77 N•m
tnet = t1 + t2 = –2.1 N•m – 0.77 N•m
tnet = –2.9 N•m
4. Evaluate
The net torque is negative,so the ball rotates in a clockwise direction.

47. Chapter 7 Simple Machines
Section 4 Torque and Simple Machines
Chapter 7
Simple Machines
A machine is any device that transmits or modifies force, usually by changing the force applied to an object.
All machines are combinations or modifications of six fundamental types of machines, called simple machines.
These six simple machines are the lever, pulley, inclined plane, wheel and axle, wedge, and screw.

48. Section 4 Torque and Simple Machines
Chapter 7
Simple Machines

49. Simple Machines, continued
Section 4 Torque and Simple Machines
Chapter 7
Simple Machines, continued
Because the purpose of a simple machine is to change the direction or magnitude of an input force, a useful way of characterizing a simple machine is to compare the output and input force.
This ratio is called mechanical advantage.
If friction is disregarded, mechanical advantage can also be expressed in terms of input and output distance.

50. Simple Machines, continued
Section 4 Torque and Simple Machines
Chapter 7
Simple Machines, continued
The diagrams show two examples of a trunk being loaded onto a truck.
In the first example, a force (F1) of 360 N moves the trunk through a distance (d1) of 1.0 m. This requires 360 N•m of work.
In the second example, a lesser force (F2) of only 120 N would be needed (ignoring friction), but the trunk must be pushed a greater distance (d2) of 3.0 m. This also requires 360 N•m of work.

51. Simple Machines, continued
Section 4 Torque and Simple Machines
Chapter 7
Simple Machines, continued
The simple machines we have considered so far are ideal, frictionless machines.
Real machines, however, are not frictionless. Some of the input energy is dissipated as sound or heat.
The efficiency of a machine is the ratio of useful work output to work input.
The efficiency of an ideal (frictionless) machine is 1, or 100 percent.
The efficiency of real machines is always less than 1.

52. Mechanical Efficiency
Section 4 Torque and Simple Machines
Chapter 7
Mechanical Efficiency

53. Chapter 7 Multiple Choice
Standardized Test Prep
Multiple Choice
1. An object moves in a circle at a constant speed. Which of the following is not true of the object?
A. Its acceleration is constant.
B. Its tangential speed is constant.
C. Its velocity is constant.
D. A centripetal force acts on the object.

54. Chapter 7 Multiple Choice
Standardized Test Prep
Multiple Choice
1. An object moves in a circle at a constant speed. Which of the following is not true of the object?
A. Its acceleration is constant.
B. Its tangential speed is constant.
C. Its velocity is constant.
D. A centripetal force acts on the object.

55. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
Use the passage below to answer questions 2–3.
A car traveling at 15 m/s on a flat surface turns in a circle with a radius of 25 m.
2. What is the centripetal acceleration of the car?
F. 2.4  10-2 m/s2
G m/s2
H. 9.0 m/s2
J. zero

56. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
Use the passage below to answer questions 2–3.
A car traveling at 15 m/s on a flat surface turns in a circle with a radius of 25 m.
2. What is the centripetal acceleration of the car?
F. 2.4  10-2 m/s2
G m/s2
H. 9.0 m/s2
J. zero

57. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
Use the passage below to answer questions 2–3.
A car traveling at 15 m/s on a flat surface turns in a circle with a radius of 25 m.
3. What is the most direct cause of the car’s centripetal acceleration?
A. the torque on the steering wheel
B. the torque on the tires of the car
C. the force of friction between the tires and the road
D. the normal force between the tires and the road

58. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
Use the passage below to answer questions 2–3.
A car traveling at 15 m/s on a flat surface turns in a circle with a radius of 25 m.
3. What is the most direct cause of the car’s centripetal acceleration?
A. the torque on the steering wheel
B. the torque on the tires of the car
C. the force of friction between the tires and the road
D. the normal force between the tires and the road

59. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
4. Earth (m = 5.97  1024 kg) orbits the sun (m =  1030 kg) at a mean distance of 1.50  1011 m. What is the gravitational force of the sun on Earth? (G =  N•m2/kg2)
F  1032 N
G  1022 N
H  10–2 N
J  10–8 N

60. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
4. Earth (m = 5.97  1024 kg) orbits the sun (m =  1030 kg) at a mean distance of 1.50  1011 m. What is the gravitational force of the sun on Earth? (G =  N•m2/kg2)
F  1032 N
G  1022 N
H  10–2 N
J  10–8 N

61. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
5. Which of the following is a correct interpretation of the expression ?
A. Gravitational field strength changes with an object’s distance from Earth.
B. Free-fall acceleration changes with an object’s distance from Earth.
C. Free-fall acceleration is independent of the falling object’s mass.
D. All of the above are correct interpretations.

62. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
5. Which of the following is a correct interpretation of the expression ?
A. Gravitational field strength changes with an object’s distance from Earth.
B. Free-fall acceleration changes with an object’s distance from Earth.
C. Free-fall acceleration is independent of the falling object’s mass.
D. All of the above are correct interpretations.

63. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
6. What data do you need to calculate the orbital speed of a satellite?
F. mass of satellite, mass of planet, radius of orbit
G. mass of satellite, radius of planet, area of orbit
H. mass of satellite and radius of orbit only
J. mass of planet and radius of orbit only

64. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
6. What data do you need to calculate the orbital speed of a satellite?
F. mass of satellite, mass of planet, radius of orbit
G. mass of satellite, radius of planet, area of orbit
H. mass of satellite and radius of orbit only
J. mass of planet and radius of orbit only

65. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
7. Which of the following choices correctly describes the orbital relationship between Earth and the sun?
A. The sun orbits Earth in a perfect circle.
B. Earth orbits the sun in a perfect circle.
C. The sun orbits Earth in an ellipse, with Earth
at one focus.
D. Earth orbits the sun in an ellipse, with the sun

66. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
7. Which of the following choices correctly describes the orbital relationship between Earth and the sun?
A. The sun orbits Earth in a perfect circle.
B. Earth orbits the sun in a perfect circle.
C. The sun orbits Earth in an ellipse, with Earth
at one focus.
D. Earth orbits the sun in an ellipse, with the sun

67. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
Use the diagram to answer
questions 8–9.
8. The three forces acting on
the wheel have equal
magnitudes. Which force will
produce the greatest torque on the wheel?
F. F1
G. F2
H. F3
J. Each force will produce the same torque.

68. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
Use the diagram to answer
questions 8–9.
8. The three forces acting on
the wheel have equal
magnitudes. Which force will
produce the greatest torque on the wheel?
F. F1
G. F2
H. F3
J. Each force will produce the same torque.

69. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
Use the diagram to answer
questions 8–9.
9. If each force is 6.0 N, the
angle between F1 and F2 is
60.0°, and the radius of the
wheel is 1.0 m, what is the
resultant torque on the wheel?
A. –18 N•m C. 9.0 N•m
B. –9.0 N•m D. 18 N•m

70. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
Use the diagram to answer
questions 8–9.
9. If each force is 6.0 N, the
angle between F1 and F2 is
60.0°, and the radius of the
wheel is 1.0 m, what is the
resultant torque on the wheel?
A. –18 N•m C. 9.0 N•m
B. –9.0 N•m D. 18 N•m

71. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
10. A force of 75 N is applied to a lever. This force lifts a load weighing 225 N. What is the mechanical advantage of the lever?
F. 1/3
G. 3
H. 150
J. 300

72. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
10. A force of 75 N is applied to a lever. This force lifts a load weighing 225 N. What is the mechanical advantage of the lever?
F. 1/3
G. 3
H. 150
J. 300

73. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
11. A pulley system has an efficiency of 87.5 percent. How much work must you do to lift a desk weighing N to a height of 1.50 m?
A J
B J
C J
D J

74. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
11. A pulley system has an efficiency of 87.5 percent. How much work must you do to lift a desk weighing N to a height of 1.50 m?
A J
B J
C J
D J

75. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
12. Which of the following statements is correct?
F. Mass and weight both vary with location.
G. Mass varies with location, but weight does not.
H. Weight varies with location, but mass does
not.
J. Neither mass nor weight varies with location.

76. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
12. Which of the following statements is correct?
F. Mass and weight both vary with location.
G. Mass varies with location, but weight does not.
H. Weight varies with location, but mass does
not.
J. Neither mass nor weight varies with location.

77. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
13. Which astronomer discovered that planets travel in elliptical rather than circular orbits?
A. Johannes Kepler
B. Nicolaus Copernicus
C. Tycho Brahe
D. Claudius Ptolemy

78. Multiple Choice, continued
Chapter 7
Standardized Test Prep
Multiple Choice, continued
13. Which astronomer discovered that planets travel in elliptical rather than circular orbits?
A. Johannes Kepler
B. Nicolaus Copernicus
C. Tycho Brahe
D. Claudius Ptolemy

79. Chapter 7 Short Response
Standardized Test Prep
Short Response
14. Explain how it is possible for all the water to remain in a pail that is whirled in a vertical path, as shown below.

80. Chapter 7 Short Response
Standardized Test Prep
Short Response
14. Explain how it is possible for all the water to remain in a pail that is whirled in a vertical path, as shown below.
Answer: The water remains in the pail even when the pail is upside down because the water tends to move in a straight path due to inertia.

81. Short Response, continued
Chapter 7
Standardized Test Prep
Short Response, continued
15. Explain why approximately two high tides take place every day at a given location on Earth.

82. Short Response, continued
Chapter 7
Standardized Test Prep
Short Response, continued
15. Explain why approximately two high tides take place every day at a given location on Earth.
Answer: The moon’s tidal forces create two bulges on Earth. As Earth rotates on its axis once per day, any given point on Earth passes through both bulges.

83. Short Response, continued
Chapter 7
Standardized Test Prep
Short Response, continued
16. If you used a machine to increase the output force, what factor would have to be sacrificed? Give an example.

84. Short Response, continued
Chapter 7
Standardized Test Prep
Short Response, continued
16. If you used a machine to increase the output force, what factor would have to be sacrificed? Give an example.
Answer: You would have to apply the input force over a greater distance. Examples may include any machines that increase output force at the expense of input distance.

85. Chapter 7 Extended Response
Standardized Test Prep
Extended Response
17. Mars orbits the sun (m = 1.99  1030 kg) at a mean distance of 2.28  1011 m. Calculate the length of the Martian year in Earth days. Show all of your work. (G =  10–11 N•m2/kg2)

86. Chapter 7 Extended Response
Standardized Test Prep
Extended Response
17. Mars orbits the sun (m = 1.99  1030 kg) at a mean distance of 2.28  1011 m. Calculate the length of the Martian year in Earth days. Show all of your work. (G =  10–11 N•m2/kg2)
Answer: 687 days

87. Centripetal Acceleration
Section 1 Circular Motion
Chapter 7
Centripetal Acceleration

88. Section 1 Circular Motion
Chapter 7
Centripetal Force

89. Section 3 Motion in Space
Chapter 7
Kepler’s Laws

90. The Magnitude of a Torque
Section 4 Torque and Simple Machines
Chapter 7
The Magnitude of a Torque

91. Section 4 Torque and Simple Machines
Chapter 7
Simple Machines