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Chapter 3 Kinematics of particles

Chapter 3 Kinematics of particles. 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

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Chapter 3 Kinematics of particles

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  1. Chapter 3 Kinematics of particles Increment: distance traveled at the end of the 1st second = 10 m distance traveled at the end of the 3rd 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). Differentiation: the ratio between two increments when they are extremely small, e.g. velocity.

  2. Position z Instantaneous velocity O y Acceleration x

  3. z y x Cartesian coordinate system

  4. 2D Polar coordination system y : unit vector // to (radial) : unit vector  to (in -direction) x O

  5. y O x radial velocity angular velocity tangential velocity Velocity Since

  6. Acceleration Since centripetal acceleration.

  7.  Solution

  8. Solution For OAP, 0.082 = 0.042 +r2+2 x 0.04 r cos Time derivative: At  = 90o, r = 0.06928 m P r 0.08m A O 0.04m

  9. z z y x r 3D Cylindrical coordination system

  10. radius of curvature  O’  O’ Normal and Tangential Coordinates (n-t) :

  11. Position of A relative to B : Velocity of A relative to B : Acceleration of A relative to B : y A B x o

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