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Unit 3, Chapter 8

Unit 3, Chapter 8. CPO Science Foundations of Physics. Chapter 9. Unit 3: Motion and Forces in 2 and 3 Dimensions. Chapter 8 Using Vectors: Forces and Motion. 8.1 Motion in Circles 8.2 Centripetal Force 8.3 Universal Gravitation and Orbital Motion. Chapter 8 Objectives.

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Unit 3, Chapter 8

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  1. Unit 3, Chapter 8 CPO Science Foundations of Physics Chapter 9

  2. Unit 3: Motion and Forces in 2 and 3 Dimensions Chapter 8 Using Vectors: Forces and Motion • 8.1 Motion in Circles • 8.2 Centripetal Force • 8.3 Universal Gravitation and Orbital Motion

  3. Chapter 8 Objectives • Calculate angular speed in radians per second. • Calculate linear speed from angular speed and vice-versa. • Describe and calculate centripetal forces and accelerations. • Describe the relationship between the force of gravity and the masses and distance between objects. • Calculate the force of gravity when given masses and distance between two objects. • Describe why satellites remain in orbit around a planet.

  4. Chapter 8 Vocabulary Terms • rotate • revolve • axis • law of universal gravitation • circumference • linear speed • angular speed • centrifugal force • radian • orbit • centripetal force • centripetal acceleration • ellipse • satellite • angular displacement • gravitational constant

  5. Key Question: How do we describe circular motion? 8.1 Vectors and Direction *Students read Section 8.1 AFTER Investigation 8.1

  6. 8.1 Motion in Circles • We say an object rotates about its axis when the axis is part of the moving object. • A child revolves on a merry-go-round because he is external to the merry-go-round's axis.

  7. 8.1 Angular Speed • Angular speed is the rate at which an object rotates or revolves. • There are two ways to measure angular speed • number of turns per unit of time (rotations/minute) • change in angle per unit of time (deg/sec or rad/sec)

  8. 8.1 Angular Speed • For the purpose of angular speed, the radian is a better unit for angles. • One radian is approx. 57.3 degrees. • Radians are better for angular speed because a radian is a ratio of two lengths.

  9. 8.1 Angular Speed Angle turned (rad) w = q t Angular speed (rad/sec) Time taken (sec)

  10. 8.1 Calculate angular speed • A bicycle wheel makes six turns in 2 seconds. • What is its angular speed in radians per second?

  11. 8.1 Linear and Angular Speed • A wheel rolling along the ground has both a linear speed and an angular speed. • A point at the edge of a wheel moves one circumference in each turn of the circle.

  12. 8.1 Linear and Angular Speed Radius (m) C = 2 Pr Circumference (m) Distance (m) 2 Pr v = d t Speed (m/sec) Time (sec)

  13. 8.1 Linear and Angular Speed Radius (m) v = w r Linear speed (m/sec) Angular speed (rad/sec) *This formula is used in automobile speedometers based on a tire's radius.

  14. 8.1 Calculate linear from angular speed • Siv is standing 4 meters from the axis of rotation and Holly is standing 2 meters from the axis. • Calculate each child’s linear speed when the angular speed of the merry go-round is 1 rad/sec. • Two children are spinning around on a merry-go-round.

  15. 8.1 Linear and Angular Speed and Displacement

  16. 8.1 Calculate angular from linear speed • The bicycle is moving forward with a linear speed of 11 m/sec. • Assume the bicycle wheels are not slipping and calculate the angular speed of the wheels in RPM. • A bicycle has wheels that are 70 cm in diameter (35 cm radius).

  17. Key Question: Why does a roller coaster stay on a track upside down on a loop? 8.2 Centripetal Force *Students read Section 8.2 AFTER Investigation 8.2

  18. 8.2 Centripetal Force • We usually think of acceleration as a change in speed. • Because velocity includes both speed and direction, acceleration can also be a change in the direction of motion.

  19. 8.2 Centripetal Force • Any force that causes an object to move in a circle is called a centripetal force. • A centripetal force is always perpendicular to an object’s motion, toward the center of the circle.

  20. 8.2 Centripetal Force Mass (kg) Linear speed (m/sec) Fc = mv2 r Centripetal force (N) Radius of path (m)

  21. 8.2 Calculate centripetal force • A 50-kilogram passenger on an amusement park ride stands with his back against the wall of a cylindrical room with radius of 3 m. • What is the centripetal force of the wall pressing into his back when the room spins and he is moving at 6 m/sec?

  22. 8.2 Centripetal Acceleration • Acceleration is the rate at which an object’s velocity changes as the result of a force. • Centripetal acceleration is the acceleration of an object moving in a circle due to the centripetal force.

  23. 8.2 Centripetal Acceleration Speed (m/sec) ac = v2 r Centripetal acceleration (m/sec2) Radius of path (m)

  24. 8.2 Calculate centripetal acceleration • A motorcycle drives around a bend with a 50-meter radius at 10 m/sec. • Find the motor cycle’s centripetal acceleration and compare it with g, the acceleration of gravity.

  25. 8.2 Centrifugal Force • We call an object’s tendency to resist a change in its motion its inertia. • An object moving in a circle is constantly changing its direction of motion. • Although the centripetal force pushes you toward the center of the circular path... • ...it seems as if there also is a force pushing you to the outside. This apparent outward force is called centrifugal force.

  26. 8.2 Centrifugal Force • Centrifugal force is not a true forceexerted on your body. • It is simply your tendency to move in a straight line due to inertia. • This is easy to observe by twirling a small object at the end of a string. • When the string is released, the object flies off in a straight line tangent to the circle.

  27. Key Question: How strong is gravity in other places in the universe? 8.3 Universal Gravitation and Orbital Motion *Students read Section 8.3 AFTER Investigation 8.3

  28. 8.3 Universal Gravitation and Orbital Motion • Sir Isaac Newton first deduced that the force responsible for making objects fall on Earth is the same force that keeps the moon in orbit. • This idea is known as the law of universal gravitation. • Gravitational force exists between all objects that have mass. • The strength of the gravitational force depends on the mass of the objects and the distance between them.

  29. 8.3 Law of Universal Gravitation Mass 1 Mass 2 F = m1m2 r2 Force (N) Distance between masses (m)

  30. 8.3 Calculate gravitational force • The mass of the moon is 7.36 × 1022 kg. • The radius of the moon is 1.74 × 106 m. • Use the equation of universal gravitation to calculate the weight of a 90 kg astronaut on the surface of the moon.

  31. A satellite is an object that is bound by gravity to another object such as a planet or star. If a satellite is launched above Earth at more than 8 kilometers per second, the orbit will be a noncircular ellipse. A satellite in an elliptical orbit does not move at a constant speed. 8.3 Orbital Motion

  32. Application: Satellite Motion

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