1. 7.3 Circular Motion and Gravity pp. 260 - 265 Mr. Richter

2. Agenda  Warm-Up  Intro to rotational motion.  Refresh on Newton’s Laws  Notes:  Centripetal Force  Centripetal Force and Inertia  Circular motion  The Myth of Centrifugal Force

3. Objectives: We Will Be Able To…  Explain how a centripetal force causes circular motion  List the factors that affect centripetal force  Describe the relationship between gravitational force, mass, and distance  Relate centripetal force to orbital motion

4. Warm-Up:

5. Centripetal Force

6.  Usually we think of a force as changing the speed of an object.  But what else can forces do?  Centripetal force is any force that is applied that changes the direction of an object but not its speed.

7. Centripetal Force  Centripetal force is applied perpendicular to the motion of an object.  It causes the object to move in a circular path.  Centripetal force always points toward the center of the circle.

8. Centripetal Force Velocity Centripetal Force

9. Centripetal Force and Inertia  Why doesn’t the ball get pulled in to the center?  Why doesn’t the ball go rocketing off in some direction?  Answer:  the ball has inertia to keep going the same speed if the force doesn’t speed it up or slow it down, and  the force is perpendicular to motion, so it only changes the ball’s direction toward the middle of the circle

10. Centripetal Force and Inertia  Force and velocity are always perpendicular to each other.  If the string is suddenly cut (or if Mr. Richter lets go), then the ball will continue in a straight-line path at a 90° angle from the string.

11. Warm-Up  A boy swings a ball in a circle on a string above his head. What factors do you think will make a difference in how much centripetal force he has to apply to keep the ball spinning in a circle?  Think and then discuss at your table. We will discuss as a class in a few minutes.

12. Centripetal Force Video  http://www.youtube.com/watch?v=PBpe_LLlQJw http://www.youtube.com/watch?v=PBpe_LLlQJw

13. Circular Motion

14.  How does the centripetal force change with the radius of the circle?  As the radius increases, the object turns more gradually, so the force required to turn the object is less. Force is inversely proportional to radius.  How does the centripetal force change with the mass of the object?  As the mass of the object increases, more force is required to cause it to turn. Force is directly proportional to mass.

15. Circular Motion  How does the centripetal force change with the speed of the object?  As the speed of an object increases, the amount of force required to turn the object increases. Force is directly proportional to the square of the speed.  Meaning:  twice as fast means four times the force required  three times as fast means nine times the force

16. Warm-Up  If the radius of an object’s orbit is doubled, by what factor does the centripetal force increase or decrease?  If the speed of an object’s orbit is quadrupled, by what factor does the centripetal force increase or decrease?

17. The Myth of Centrifugal Force

18. The Rotor Ride  http://www.youtube.com/watch?v=Or0IFpRSTjM http://www.youtube.com/watch?v=Or0IFpRSTjM

19. The Rotor Ride  Explain what you think is happening on the rotor ride you saw. Is there really a force coming from the middle of the ride, pushing people against the wall? If not, what do you think is really happening?  Discuss at your table and we will discuss in a few minutes.

20. The Myth of “Centrifugal Force”  It might seem like as an object is rotating, there is a force pushing the object away from the center of the circle.  THIS IS NOT TRUE. THERE IS NO SUCH THING AS CENTRIFUGAL FORCE! There is no force pushing away from the center of the circle.  Objects just want to keep going in a straight line. Inertia, not force.

21. Gravitational Force Does the moon pull on the earth?

22. Gravitational Force  Newton observed that some centripetal force must be required to cause planets and moons to orbit in a circle.  He determined that this force must be gravity!  Gravity is a form of centripetal force!  The force of gravity between two objects is the same in both directions.  The moon pulls on Earth the same as Earth pulls on the moon.

23. Gravitational Force  Gravitational force exists between ALL objects that have mass.  Your weight is the force of gravity between you and the Earth.  This force changes if you travel to another planet, get farther from the earth, or go to the moon.  It takes an enormous amount of mass to have a noticeable force of gravity.

24. Gravitational Force  The gravitational force between two objects always lies along the line connecting their centers.  The size of the force depends on:  The mass of each object: as masses increase, the force of gravity increases.  The distance between the objects from center to center: force decreases with the square of the distance.

25. Think About It  According to the Law of Universal Gravitation formula, will you weigh more or less (or the same) on the top of Mt. Everest?

26. Note: Measuring Distance  We measure distance between two objects from their centers:  NOT because gravity comes from the center of objects. ALL of the object’s mass contributes to the force of gravity.  The center is your average distance to all parts of the object.

27. Calculating the Force of Gravity  Newton’s Law of Universal Gravitation gives the relationship between gravitational force, distance, and the masses of any two objects.  G is the gravitational constant:  6.67 x 10 -11 N  m 2 /kg 2 Note: because G is so small, at least one mass needs to be very large to have much gravitational force.

28. Your Turn  Use the following information to calculate the force of gravity between Earth and the moon.  Mass of Earth: 5.97 × 10 24 kg  Mass of moon: 7.34 × 10 22 kg  Distance between centers of Earth and moon: 3.84×10 8 m  Answer: 1.99 x 10 20 N

29. Practice  Calculate the force between two objects that have masses of 70 kilograms and 2,000 kilograms separated by a distance of 1 meter.  A man on the moon with a mass of 90 kilograms weighs 146 newtons. The radius of the moon is 1.74 x 10 6 meters. Find the mass of the moon.

30. Wrap-Up: Did we meet our objectives?  Explain how a centripetal force causes circular motion  List the factors that affect centripetal force  Describe the relationship between gravitational force, mass, and distance  Relate centripetal force to orbital motion

31. Homework  Due Monday  p265 Gravitational Force #1-3  p265 Section Review #1, 3  p 270 #34, 36  Boooooks!