11/03

1. 11/03 1. Which moves faster on a merry-go-round, a horse near the outside rail or one near the inside rail? 2. If the hamster stops running does it rotate or does in revolve?

2. Close reading procedure 1. FIRST READ (Key Ideas & Details) • read text - Think-Pair-Share to check understanding 2. SECOND READ (Craft & Structure) • Number the paragraphs • Circle main vocabulary, underline main points, add question marks and exclamation • Think Aloud, Shared, Paired, portions of text that will aid in citing text based evidence • Discuss in small and whole group 3. THIRD READ (Integration of Knowledge and Ideas) • Reread (with a group) selected chunk focusing on text dependent question use pencils to mark text • find parts of text that will aid in citing – (text based evidence) • Discuss in small and whole group • Journaling with text dependent question

3. Uniform Circular Motion and Centripetal Acceleration 5.1 and 5.2

4. Centripetal force keeps an object in circular motion.

5. 10.1Rotation and Revolution Earth undergoes both types of rotational motion. • It revolves around the sun once every 365 ¼ days. • It rotates around an axis passing through its geographical poles once every 24 hours.

7. Uniform Circular Motion • Period(T) – Time it takes to make one trip around the circle • Circumference – distance around the circle • C = 2r • Object is traveling at a constant (uniform) speed on a circular path

8. 10.2Rotational Speed The turntable rotates around its axis while a ladybug sitting at its edge revolves around the same axis. Linear speed is the distance traveled per unit of time. • Tangential speed – the linear speed of an object along a circular path The greater distance from the axis the greater the tangential speed

9. 10.2Rotational Speed Tangential and Rotational Speed Tangential speed and rotational speed are related. Tangential speed is directly proportional to the rotational speed and the radial distance from the axis of rotation. Tangential Velocity ~ radial distance × rotational speed Vt = r * w

10. 10.2Rotational Speed In symbol form, v ~ r where v is tangential speed and  (pronounced oh MAY guh) is rotational speed. • You move faster if the rate of rotation increases (bigger ). • You also move faster if you are farther from the axis (bigger r).

11. Uniform Circular Motion • Speed (v) – distance / time • Find v • v = 3.77 m/s 1.2 m T=2s

12. Uniform Circular Motion • Speed is constant • Velocity is not constant • Velocity is always changing • This acceleration is “centripetal” acceleration

13. 5.2 Centripetal Acceleration • Object moves in circular path • At time t0 it is at point O with a velocity tangent to the circle • At time t, it is at point P with a velocity tangent to the circle • The radius has moved through angle 

14. Centripetal Acceleration • Draw the two velocity vectors so that they have the same tails. • The vector connecting the heads is v • Draw the triangle made by the change in position and you get the triangle in (b)

15. Centripetal Acceleration • Since the triangles have the same angle are isosceles, they are similar

16. Centripetal Acceleration

17. Centripetal Acceleration Know this

18. Centripetal Acceleration

19. Forces cause acceleration • F=ma • Ac = V2 / r centripetal acceleration • Fc = m (v2 / r) centripetal force

20. Centripetal acceleration – acceleration toward the center • Centripetal force – a center directed force that causes an object to move in a curved path • Gravity provides constant centripetal force

21. 11/4 1. A 20 kg child is on the merry go round. If she is 3 m from the center of the merry go round and her tangential velocity is 2 m/s what is her centripetal acceleration? Which equation are you using? 2. When a can is twirled in a circle, what is the direction of acceleration? Today : Spinning stopper lab

22. What are the variables that can be changed in the spinning stopper? • What do you think affects the rate at which the stopper spins?

23. Centripetal Acceleration • At any given moment • v is pointing tangent to the circle • ac is pointing towards the center of the circle • If the object suddenly broke from circular motion would travel in line tangent to circle

24. 10.3Centripetal Force Calculating Centripetal Forces Greater speed and greater mass require greater centripetal force. Traveling in a circular path with a smaller radius of curvature requires a greater centripetal force. Centripetal force, Fc, is measured in newtons when m is expressed in kilograms, v in meters/second, and r in meters.

25. 11/5 • What two forces where acting on the stopper allowing it to stay suspended? • What happens to the period (time to complete a rotation) as your radius decreases? • What can you do if you want to know if your data is accurate?

26. Spinning stopper lab write up • Claim – how where you able to suspend the stopper (2 forces) • Evidence – calulations, data table, observations • Reasoning – discuss centripetal force, what was acting on the small mass to keep it orbiting? Vocabulary : Direction, gravity, Explain centripetal force, centripetal acceleration in terms of equations.

27. 11/6 • How many cm long is your pinky? • How many meters is in 10 cm? Due today – circular motion write up

28. See metric mania • Untitled – ne - measurement

29. myth busters full episodes circular motion • http://www.youtube.com/watch?v=torrlSW6VnA • http://www.youtube.com/watch?v=B5LCTVK8kDs&list=PL78DB5CFC40BE2225 • http://www.youtube.com/watch?v=d3FrvV3It5U can you do a 360 degree swing? This claims that you can

30. http://www.youtube.com/watch?v=PBpe_LLlQJw

31. Example 1 • Two identical cars are going around two corners at 30 m/s. Each car can handle up to 1 g. The radius of the first curve is 50m and the radius of the second is 100 m. Do either of the cars make the curve? (hint find the ac) • Yes, 100m 50 m 100 m

32. Problems • Try this • Concept development practice page 9-2

33. Which arrow indicates the direction of the gravitational force the star exerts on the comet when the comet is in the position shown? • 1 • 2 • 3 • 4

34. A tin can spun around on the end of a string moves in circle because • a. once the can starts moving, that is its natural tendency • b. the can continually pulls on the string • c. there is a force on the can pulling outward • d. the string continually pulls inward on the can

35. (8.4) Suppose a 30kg child is riding a merry go round. If she is 2.00m from the center of the merry go round and her tangential velocity is 2.50 m/s, what is her centripetal acceleration? • a. 5.00m/s2 • b. 3.12m/s2 • c. 281m/s2 • d. 1.25m/s2

37. 4/14 Due today: Stopper lab CER • What determines how fast a planet revolves around the sun? mass, size, or distance from the sun? • How long does it take the moon to orbit the earth? What would happen to the period if the moon where farther from the earth?

38. 14.2Circular Orbits Describe the motion of a satellite in relation to Earth’s surface and gravity.

39. 14.3Elliptical Orbits A simple method of constructing an ellipse is shown here.

40. 14.3Elliptical Orbits • What happens if you launch a satellite at 9 km/s • Satellite speed varies in an elliptical orbit. • When the initial speed is more than 8 km/s, the satellite overshoots a circular path and moves away from Earth. • It loses speed due to the pull of gravity. • The satellite slows to a point where it no longer recedes, and begins falling back toward Earth.

41. 14.3Elliptical Orbits • A satellite moves in an elliptical orbit. • When the satellite exceeds 8 km/s, it overshoots a circle.

42. 14.3Elliptical Orbits • A satellite moves in an elliptical orbit. • When the satellite exceeds 8 km/s, it overshoots a circle. • At its maximum separation, it starts to come back toward Earth.

43. 14.3Elliptical Orbits • A satellite moves in an elliptical orbit. • When the satellite exceeds 8 km/s, it overshoots a circle. • At its maximum separation, it starts to come back toward Earth. • The cycle repeats itself.

44. 14.3Elliptical Orbits • The parabolic paths of projectiles, such as cannonballs, are actually segments of ellipses. • For relatively low speeds, the center of Earth is the far focus.

45. 14.3Elliptical Orbits • The parabolic paths of projectiles, such as cannonballs, are actually segments of ellipses. • For relatively low speeds, the center of Earth is the far focus. • For greater speeds, the near focus is Earth’s center.

46. 14.4Energy Conservation and Satellite Motion For a satellite in circular orbit, no force acts along the direction of motion. The speed, and thus the KE, cannot change.

47. 14.3Elliptical Orbits think! The orbit of a satellite is shown in the sketch. In which of the positions A through D does the satellite have the greatest speed? The least speed?Answer: The satellite has its greatest speed as it whips around A. It has its least speed at C. Beyond C, it gains speed as it falls back to A to repeat its cycle.

48. 14.3Elliptical Orbits think! The orbit of a satellite is shown in the sketch. In which of the positions A through D does the satellite have the greatest speed? The least speed?

49. 14.3Elliptical Orbits What is the shape of the path of a satellite in an orbit around Earth?

50. Conservation of energy total energy stays the same • Total energy = kinetic energy + potential energy • Kinetic energy = energy due to speed • Potential energy = energy due to distance