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Mastering Kinematics: From Fundamental to Derived Quantities

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Delve into the world of physics kinematics, exploring fundamental and derived quantities, significant figures, scientific notation, measurement tools, accuracy, precision, velocity, acceleration, and uniformly accelerated motion.

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Mastering Kinematics: From Fundamental to Derived Quantities

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  1. Physics Beyond 2000 Chapter 1 Kinematics

  2. Physical Quantities • Fundamental quantities • Derived quantities

  3. Fundamental Quantities http://www.bipm.fr/

  4. Derived Quantities • Can be expressed in terms of the basic quantities • Examples • Velocity • Example 1 • Any suggestions?

  5. Derived Quantities • More examples

  6. Standard Prefixes • Use prefixes for large and small numbers • Table 1-3 • Commonly used prefixes • giga, mega, kilo • centi, milli, micro, nana, pico

  7. Significant Figures The number of digits between the Most significant figure and least significant figure inclusive. • The leftmost non-zero digit is the most significant figure. • If there is no decimal point, the rightmost non-zero digit will be the least significant figure. • If there is a decimal point, the rightmost digit is always the least significant figure.

  8. Scientific Notation • Can indicate the number of significant numbers

  9. Significant Figures • Examples 5 and 6. • See if you understand them.

  10. Significant Figures • Multiplication or division. • The least number of significant figures. • Addition or subtraction. • The smallest number of significant digits on the right side of the decimal point.

  11. Order of Magnitude • Table 1-4.

  12. Measurement • Length • Meter rule • Vernier caliper • Micrometer screw gauge Practice

  13. Measurement • Time interval • Stop watch • Ticker tape timer • Timer scaler

  14. Measurement • Mass • Triple beam balance • Electronic balance

  15. Measurement • Computer data logging

  16. Error Treatment • Personal errors • Personal bias • Random errors • Poor sensitivity of the apparatus • System errors • Measuring instruments • Techniques

  17. Accuracy and Precision • Accuracy • How close the measurement to the true value Precision • Agreement among repeated measurements • Largest probable error tells the precision of the measurement

  18. Accuracy and Precision • Examples 9 and 10

  19. Accuracy and Precision • Sum and difference • The largest probable error is the sum of the probable errors of all the quantities. • Example 11

  20. Accuracy and Precision • Product, quotient and power • Derivatives needed

  21. Kinematics • Distance d • Displacement s

  22. Average Velocity • Average velocity = displacement  time taken

  23. Instantaneous Velocity • Rate of change of displacement in a very short time interval.

  24. Uniform Velocity • Average velocity = Instantaneous velocity when the velocity is uniform.

  25. Speed • Average speed • Instantaneous speed

  26. Speed and Velocity • Example 13

  27. Relative Velocity • The velocity of A relative to B • The velocity of B relative to A

  28. Relative Velocity • Example 14

  29. Acceleration • Average acceleration • Instantaneous acceleration

  30. Average acceleration • Average acceleration = change in velocity  time Example 15

  31. Instantaneous acceleration Example 16

  32. v t Velocity-time graphv-t graph Slope: = acceleration

  33. v-t graph • Uniform velocity: slope = 0 v t

  34. v-t graph • Uniform acceleration: slope = constant v t

  35. Falling in viscous liquid Acceleration Uniform velocity

  36. Falling in viscous liquid v uniform speed: slope = 0 acceleration: slope=g at t=0 t

  37. Bouncing ball with energy loss Let upward vector quantities be positive. Falling: with uniform acceleration a = -g.

  38. v-t graph of a bouncing ball • Uniform acceleration: slope = -g v t falling

  39. Bouncing ball with energy loss Let upward vector quantities be positive. Rebound: with large acceleration a.

  40. v-t graph of a bouncing ball • Large acceleration on rebound v rebound t falling

  41. Bouncing ball with energy loss Let upward vector quantities be positive. Rising: with uniform acceleration a = -g.

  42. v-t graph of a bouncing ball • Uniform acceleration: slope = -g v rebound rising t falling

  43. v-t graph of a bouncing ball The speed is less after rebound • falling and rising have the same acceleration: slope = -g v rebound rising t falling

  44. Linear Motion: Motion along a straight line • Uniformly accelerated motion: a = constant velocity v u time 0 t

  45. Uniformly accelerated motion • u = initial velocity (velocity at time = 0). • v = final velocity (velocity at time = t). • a = acceleration v = u + at

  46. Uniformly accelerated motion • = average velocity velocity v u time 0 t

  47. Uniformly accelerated motion s = displacement = velocity v u time 0 t s = area below the graph

  48. Equations of uniformly accelerated motion

  49. Uniformly accelerated motion • Example 17

  50. Free falling: uniformly accelerated motion Let downward vector quantities be negative a = -g

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