1. Jump to first page 1 Chapter 3 Kinematics of particles Differentiation: the ratio between two increments when they are extremely small, e.g. velocity. Increment: distance traveled at the end of the 1 st second = 10 m distance traveled at the end of the 3 rd second = 14 m increment of distance = 4 m increment of time = 2 s Ratio between two increments = 4 m/2s = 2 m/s (average velocity) More detailed measurement: distance traveled at the end of 1.01 second, the distance traveled is 10.025 m, the ratio becomes 0.025 m / 0.01 s = 2.5 m/s (instantaneous velocity).

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3. 3

4. 4 y x z O Instantaneous velocity Acceleration Position

5. Jump to first page 5 Cartesian coordinate system x z y

6. Jump to first page 6 2D Polar coordination system y x O : unit vector // to (radial) : unit vector  to (in  -direction)

7. Jump to first page 7 Velocity Since radial velocity tangential velocity angular velocity O x y

8. Jump to first page 8 centripetal acceleration. Acceleration Since

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10. Solution  

11. Jump to first page 11 0.08m 0.04m P A O r Solution For  OAP, 0.08 2 = 0.04 2 +r 2 +2 x 0.04 r cos  Time derivative: At  = 90 o, r = 0.06928 m

12. Jump to first page 12 3D Cylindrical coordination system x z y z r

13. Jump to first page 13 Normal and Tangential Coordinates (n-t) :  radius of curvature O’ 

14. Jump to first page 14 Position of A relative to B : Velocity of A relative to B : Acceleration of A relative to B : A B o x y