Dimensions of Physics

1. Dimensions of Physics

2. The essence of physics is to measure the observable world and describe the principles that underlie everything in creation. This usually involves mathematical formulas.

3. The Metric System • first established in France and followed voluntarily in other countries • renamed in 1960 as the SI (Système International d’Unités) • seven fundamental units

4. Dimension • can refer to the number of spatial coordinates required to describe an object • can refer to a kind of measurable physical quantity

5. Dimension • the universe consists of three fundamental dimensions: • space • time • matter

6. Length • the meter is the metric unit of length • definition of a meter: the distance light travels in a vacuum in exactly 1/299,792,458 second.

7. Time • defined as a nonphysical continuum that orders the sequence of events and phenomena • SI unit is the second

8. Mass • a measure of the tendency of matter to resist a change in motion • mass has gravitational attraction

9. The Seven Fundamental SI Units • length • time • mass • thermodynamic temperature • meter • second • kilogram • kelvin

10. The Seven Fundamental SI Units • amount of substance • electric current • luminous intensity • mole • ampere • candela

11. SI Derived Units • involve combinations of SI units • examples include: • area and volume • force (N = kg • m/s²) • work (J = N • m)

12. Conversion Factors • any factor equal to 1 that consists of a ratio of two units • You can find many conversion factors in Appendix C of your textbook.

13. 18 m Unit Analysis First, write the value that you already know.

14. Unit Analysis Next, multiply by the conversion factor, which should be written as a fraction. 100 cm 1 18 m × m Note that the old unit goes in the denominator.

15. Unit Analysis Then cancel your units. 100 cm 1 18 m × m Remember that this method is called unit analysis.

16. = 1800 cm Unit Analysis Finally, calculate the answer by multiplying and dividing. 100 cm 1 18 m × m

17. Unit Analysis Bridge

18. Sample Problem #1 1 km 1000 m × 13.4 km = Convert 13400 m to km. 13400 m

19. Sample Problem #2 7 d 1 wk 24 h 1 d 60 min 1 h × × × = 604,800 s 60 s 1 min × How many seconds are in a week? 1 wk

20. Sample Problem #3 1 mi 1.6 km ≈ × 21.9 mi Convert 35 km to mi, if 1.6 km ≈ 1 mi. 35 km

21. Principles of Measurement

22. Instruments • tools used to measure • critical to modern scientific research • man-made

23. Accuracy • comparing the object being measured to the graduated scale of an instrument

24. Accuracy • dependent upon: • quality of original design and construction • how well it is maintained • reflects the skill of its operator

25. Error • the simple difference of the observed and accepted values • may be positive or negative

26. Error • absolute error—the absolute value of the difference

27. observed – accepted accepted × 100% Percent Error

28. Precision • a qualitative evaluation of how exactly a measurement can be made • describes the exactness of a number or measured data

29. Precision • some quantities can be known exactly • definitions • countable quantities

30. Precision • irrational numbers • can be specified to any degree of exactness desired • potentially unlimited precision

31. When you use a mechanical metric instrument (one with scale subdivisions based on tenths), measurements should be estimated to the nearest 1/10 of the smallest decimal increment.

32. The last digit that has any significance in a measurement is estimated.

33. Truth in Measurements and Calculations

34. Significant Digits Remember: The last (right-most) significant digit is the estimated digit when recording measured data.

35. Significant Digits Rule 1: SD’s apply only to measured data.

36. Significant Digits Rule 2: All nonzero digits in measured data are significant.

37. Significant Digits Rule 3: All zeros between nonzero digits in measured data are significant.

38. Significant Digits Rule 4: For measured data containing a decimal point: • All zeros to the right of the last nonzero digit (trailing zeros) are significant

39. Significant Digits Rule 4: For measured data containing a decimal point: • All zeros to the left of the first nonzero digit (leading zeros) are not significant

40. Significant Digits Rule 5: For measured data lacking a decimal point: • No trailing zeros are significant

41. Significant Digits Scientific notation shows only significant digits in the decimal part of the expression.

42. Significant Digits A decimal point following the last zero indicates that the zero in the ones place is significant.

43. ...and be careful when using your calculator!

44. Adding and Subtracting Rule 1: All units must be the same before you can add or subtract.

45. Adding and Subtracting Rule 2: The precision cannot be greater than that of the least precise data given.

46. Multiplying and Dividing Rule 1: A product or quotient of measured data cannot have more SDs than the measurement with the fewest SDs.

47. Multiplying and Dividing Rule 2: The product or quotient of measured data and a pure number should not have more or less precision than the original measurement.

48. Compound Calculations Rule 1: If the operations are all of the same kind, complete them before rounding to the correct significant digits.

49. Compound Calculations Rule 2: If the solution to a problem requires a combination of both addition/subtraction and multiplication/division...

50. Compound Calculations (1) For intermediate calculations, underline the estimated digit in the result and retain at least one extra digit beyond the estimated digit. Drop any remaining digits.