1. Physics （ Fifth Edition · Part I ） Shanghai Normal university. Department of Physics

2. Chapter 1 The Kinematics of Mass Points §1.1 The Description of the Motion of Mass pointsThe Description of the Motion of Mass points §1.2 Motion in a CircleMotion in a Circle §1.3 Relative MotionRelative Motion Summary

3. §1.The description of the Motion of Mass Points 1. Refernce frame, mass pointRefernce frame, mass point 2. Position vector, equation of motion and displacementPosition vector, equation of motion and displacement 3. VelocityVelocity 4. AccelerationAcceleration

4. 1 Reference frames, mass point To determine the location of a body at the reference object quantitatively, a coordinate system is built on it. 1 Reference frames To describe the position of an object, the other object referred to (Reference Frame ） should be chosen. It is arbitrary. 2 Mass point If we may ignore object’s size and shape, we may regard the object as a single point with a mass, such a point is usually called a mass point.

5. 坐标系 r φ θ plante The normal unite vector The tangential unite vector A moving mass point τ n Natural coordinate system Spherical coordinate system Cartesian coordinate system

6. 2 Position vector, equation of motion and displacement 1 position vector The absolute value of The location of a particle P relative to the origin of a coordinate system, represented by the position vector. Direction cosines of

7. 随时 间变化 Component equations 2 Equation of Motion Trajectory Equation: by eliminating the parameter t 2 Position vector, equation of motion and displacement

8. B A B A The displacement vector extends from the head of the initial position vector to the head of the later position vector. 2 Position vector, equation of motion and displacement 3.Displacement—A particle is changing in its position:

9. the length of this vector, i.e. B A Consquently the displacement can be described with three components in Cartesian coordinate O-xyz and 2 Position vector, equation of motion and displacement 4 Path （ ） : the actual trajectory of the mass point.

10. Physical meaning of displacement A) Displacement depends only on the initial and final position the object, it is independent of the real path B ） showing the properties of vector and superposition of movement notes The changing of the radial length of displacement 2 Position vector, equation of motion and displacement

11. The displacement and the path （ B ） in general case, the displacement is not equal to the distance. （ D ） displace is a vector, path is a scalar. (C) under what case ？ Move in straight line without changing direction; In the limit as. discuss （ A ） the path between P 1 P 2 are not only ， e.g. or, but the displacement are unique.

12. The and have the same direction Magnitude is B A 1 Average velocity in the time interval ， the mass point moving from A to B ， the displacement is The Average velocity is Or 3 velocity

13. 2 Instantaneous velocities at every point along the trajectory, the instantaneous velocity vector is tangent to the trajectory at that point. as,the limit of the average velocity is called the instantaneous velocity ， as ， 3 velocity

14. instantaneous speed ： the magnitude of instantaneous velocity The velocity of a mass point in 3- D Cartesian coordinate system is 3 velocity

15. Average Speed: B A Instantaneous: discuss A mass point is at the endpoint of the position vector at instantaneous time t, the speed is ( ) （A）（A） （B）（B）（C）（C） （D）（D） （E）（E） 3 velocity

16. Example 1 let the equation of motion be Where, （ 1 ） what is the velocity at. ( 2 ) plot the trajectory of the mass. solution （ 1 ） the following velocity components The velocity vector is The angle with the respect to the position x-axis is

17. （ 2 ） equation motion The trajectory equation can be got by eliminating t 0 轨迹图 246- 6- 4- 2 2 4 6

18. Example 2 as illustrated in following figure ， A 、 B are connected by a thin rod with length ， A and B may slide along smooth tracks. If A slide at a constant speed toward left, when, what is the velocity of object B Solution Based on the coordinate system of figure, the velocity of object A is OAB is a rectangle triangle ， the length l of the rigid thin rod is a constant A B l the velocity of object B is

19. A B l Furthermore yield The direction of points to the positive direction of the y axis ， when,

20. 1 ） average acceleration B and have the same direction. the velocity increment per unit time 2) (instantaneous) acceleration 4 Acceleration A

21. Magnitude is acceleration Magnitude of ā The acceleration in 3-D coordination is 4 Acceleration

22. ？ 讨论 intercepted in Ob Yield The change of direction of the velocity The change of the magnitude of the velocity 4 Acceleration

23. O If ？ discussion given So, we can get Example circular motion with constant speed so and

24. Geting integral constant according with initial condition Two kinds of questions in Kinematics:

25. Solution ： according the definition of acceleration Example 3 a ball drops vertically in a liquid,the initial velocity of the ball is ， its acceleration is. Question: 1 ） after how long can the ball be considered as no longer moving? And (2) how long has the ball gone through before stopping ？

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27. p.50 / 1- 8, 9, 13, 17 Homework

28. §1.2 Motion in a Circle 1. Planar polar coordinate systemPlanar polar coordinate system 2. Angular velocity of the circular motionAngular velocity of the circular motion 3. Tangential and normal acceleration ofTangential and normal acceleration of circular motion, angular acceleration 4. Circular motion with constant speed and circular motion with constant variation of sppedCircular motion with constant speed and circular motion with constant variation of spped

29. 1 Planar polar coordinate system A Assume a mass point moves on the ， at some moment it is at point A.the angle between the directional line segment pointing from the coordinate origin O to point A and the axis is. The point A can be determined by is called the planar polar coordination system. The transformation relationship between these two coordinate systems

31. 2 Angular velocity and angular acceleration of the circular motion Angular velocity angular coordinate Angular acceleration Speed A B

32. The circular motion Tangential acceleration The variation rate of normal unite vector with respect to time Normal unit vector 3 Tangential and normal acceleration of the circular motion

33. Tangential acceleration （ caused by magnitude variation of the velocity ） Normal acceleration （ originated from the direction change of the velocity ） 3 Tangential and normal acceleration of the circular motion

34. Tangential acceleration decreasing increasing 3 Tangential and normal acceleration of the circular motion

35. For General curve Motion （ natural coordinate system ） where is curvature radius. 3 Tangential and normal acceleration of the circular motion

36. 4 Circular motion with constant speed and circular motion with constant variation rate of speed 1 circular motion with constant speed ： speed and angular velocity are both constants. 2 circular motion with constant variation rate of speed when, constant Angular acceleration 3 Tangential and normal acceleration of the circular motion

37. For a object with a curved shape motion ， which one is the correct among the following statement ： （ A ） Tangential acceleration definitely does not zero ； （ B ） Normal acceleration definitely does not zero （ except for the point of extremum ）； （ C ） For the direction of the velocity is same the tangential direction, and normal speed definitely does zero ， so normal acceleration is definitely zero ； （ D ） A mass point is in a line motion with constant speed ， the acceleration is definitely zero; （ E ） If the acceleration is a invariable vector ， it must be carry out a motion with constant variation rate of speed. discussion

38. A B Example the horizontal speed of supersonic fighter jet at a high altitude point A is 1940 km/h, drives along a curve similar to a circular are to the point B, its speed at B is 2192 km/h, the time lapse is 3s, assume the radius of the arc AB is approximately 3.5km, and the process of driving from A to B can be considered as circular motion with constant variation rate, if the gravitational acceleration can be ignored, what are (1) the acceleration of the fighter jet at point B and,(2)the real distance the fighter jet goes through from point A to point B?. Solution （ 1 ） the tangential acceleration and are the constant.

39. A B Given ： The normal acceleration at B point The magnitude of acceleration is the angle is

40. Given ： （ 2 ） in time, the angle swept out by is The distance the jet goes through is Putting the date, we have A B

41. §1.3 Relative motion 一. Time and spaceTime and space 二. Relative motionRelative motion Example

42. 1 Time and space I n the two reference frames moving relative to each other, the measurement of length is absolute, regardless of the reference frame. The absoluteness of the time and the length is the foundation of classical or Newton’s mechanics A B a wagon moves with a relatively slow velocity along the horizontal tracks and goes through point A and B. The time the wagon takes to go from point A to B is the same measured by passenger standing on the wagon and by a ground observer, respectively.

43. 相对运动 Relative motion The ball is in a curved shape motion The ball is in a linemotion at perpendiculardirection How to transformation ？ The motion status of the object depends on the selection of the reference frame 1 Time and space

44. * Transformation relationship of velocity Relationship of the displacement P S frame frame 1 Time and space

45.  Galileo velocity transformation formula Notes If the velocity of the mass point approaches to the speed of the light, Galileo velocity transformation can no longer be applied for The absolute velocity （ observed in S frame ） The relative velocity （ observed in S’ frame ） Convected velocity （ the speed of moving frame S’ relative to the basic reference frame S ） 2 Relative motion

46. Example As shown in figure, an experimentalist A controls a bullet launcher on a flat car that moves with a constant speed of 10 m/s along a horizontal track. The launcher fires a bullet with a projectile angle in the opposite direction the cart moving. Another experimentalist B on the ground observes that the bullet moves vertically up, what is the height that the bullet can reach? A B Using velocity transformation formula Solution the ground reference frame is S with the coordinate system Oxy, and the cart reference frame is S’ frame

47. The height is A B

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49. Chapter 1 Summary

50. Review

51. Geting integral constant according with initial condition Two kinds of questions in Kinematics:

52. The end