1. Tarzan 泰山 vine 藤

4. Instantaneous momentum principle

5. Newton’s Second Law of Motion (Momentum Principle) instantaneous rate of change of momentum 变化率 We now know at least four different way of writing this law…

6. Rules for identifying forces (1)Choose a system. (2) Distance forces: Show all forces due to objects in the surroundings that interact with the system at a distance (gravitationally or electrically). (3) Contact forces: Show all forces due to objects in the surroundings that are touching the system.

8. What objects exert significant forces on the red block? 1) Earth, String 1, String 2 2) Earth, String 1, String 2, Hand 3) Earth, String 1, String 2, Hand, Ceiling 4) Earth, Hand, Ceiling Your turn…

9. F 1 and F 2 are magnitudes of forces. What is the unit vector in the direction of the force? 1) 2) 3) 4)

10. Your turn… F 1 and F 2 are magnitudes of forces. Which equation correctly states that dp x /dt = Fnet x ? 1) 0 = – F 1 *cos(  ) + F 2 2) 0 = F 1 – F 2 3) 0 = F 1 + F 2 – mg 4) 0 = F 1 *cos(90+  ) + F 2

11. Your turn… F 1 and F 2 are magnitudes of forces. Which equation correctly states that dp y /dt = Fnet y ? 1) 0 = F 1 – mg 2) 0 = F 1 + F 2 – mg 3) 0 = – F 1 *cos(  ) + F 2 4) 0 = F 1 *cos(  ) – mg

12. Rules for finding the rate of change of momentum (1)Draw two arrows: - one for, the momentum a short time before the moment of interest; - one for, the momentum a short time after the moment of interest (2) Find (3) The direction of is the same as the direction of.

13. Your turn… A ball hangs from the bottom of a vertical spring. You pull the ball downwards and release it, and the ball oscillates up and down. At the bottom of each oscillation, where the ball’s instantaneous momentum is zero, what is the direction of ?

14. Your turn… A ball hangs from the bottom of a vertical spring. You pull the ball downwards and release it, and the ball oscillates up and down. At the bottom of each oscillation, where the ball’s instantaneous momentum is zero, what is the direction of ?

16. Comet 彗星

17. Which of the red arrows labeled 1, 2, or 3 represents the vector, the change in the momentum of the comet? Your turn…

18. Comet simulation…

19. Change of momentum can be split into two parts: (1) Parallel to the momentum (change of speed) (2) Perpendicular to the momentum (change of direction)

20. Changes speed Changes direction

21. Ball and mallet video…

24. kissing circle Bigger force, smaller radius. Bigger momentum, bigger radius.

25. Your turn… The Moon travels in a nearly circular orbit around the Earth, at nearly constant speed. When the Moon is at location A, which components of are zero? 1) The parallel component 2) The perpendicular component 3) Both the parallel and perpendicular components 4) Neither component

26. Here’s the proof… Analytical solution for the rate of change of direction: radius of “kissing circle”

27. Parallel to momentum Perpendicular to momentum

28. θ R R After a time Δt, particle moves to position 2. RR θ θ 1 1 These are similar triangles.

29. θ R R After a time Δt, particle moves to position 2. RR θ These are similar triangles. θ 11

30. These are similar triangles, so: RR θ θ 11 limit Δt -> 0

31. These are similar triangles, so: limit Δt -> 0

32. Example… What is the speed of a satellite ( 卫星 ) in a circular orbit ( 轨道 ) of radius R around the Earth?

33. Back to Tarzan… Why does the vine break?

34. Tarzan swings from a vine. At the bottom of the swing, what is the direction of his ? Your turn…

35. Tarzan swings from a vine. At the bottom of the swing, what is the direction of the net force on Tarzan?

36. Your turn… Tarzan swings from a vine. At the bottom of the swing, what objects exert forces on Tarzan? 1) Earth, vine 2) centrifugal force ( 离心力 ) only 3) Earth and centrifugal force 4) Earth, vine, centrifugal force

37. Your turn… At the bottom of the swing, how does the magnitude of the force on Tarzan by the vine compare to the magnitude of the force on Tarzan by the Earth? 1 ) F vine > F Earth 2) F vine = F Earth 3) F vine < F Earth 4) Not enough info.

38. Your turn… - Tarzan's mass: 100 kg. - Length of vine: 5 m. - Tarzan's speed: 13 m/s. What is the tension in the vine at this instant? 1) 980 N 2) 3380 N 3) 2400 N 4) 4360 N

39. QUIZ