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. Unit of measurement – the unit being measured Pure number – the number of units determined by the act of measuring Measurement – the product of the pure number and the unit of measurement Measurements - Quantitative

13. 4 feet extra large Hot 100 ºF Sunny 96 Your Turn to Decide

14. 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.

15. 18 m Unit Analysis First, write the value that you already know.

16. 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.

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

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

19. Unit Analysis Bridge

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

21. 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

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

23. Converts from one unit to another Conversion Factor – a fraction (ratio) comparing two units Examples: 12 inches = 1 foot 3 feet = 1 yard 100 cm = 1 m 60 s = 1 min Conversion factors can be inverted!! Dimensional Analysis

24. Grid Method for Conversions

25. Grid Method for Conversions Convert 8.4 miles to feet.

26. Grid Method for Conversions Convert 8.4 miles to feet.

27. Dimensional Analysis How many days is equal to 14 x 1018 s?

28. Quantitative- use numbers to describe Easy to verify Easy to agree upon, no personal bias The measuring instrument limits how good the measurement is Qualitative- use description without numbers Types of measurement

29. Scientists use two words to describe how good the measurements are Accuracy- how close the measurement is to the actual value Precision- how well can the measurement be repeated How good are the measurements?

30. Accuracy can be true of an individual measurement or the average of several Precision requires several measurements before anything can be said about it Example Differences

31. Let’s use a golf analogy.

32. Accurate? No Precise? Yes

33. Accurate? Yes Precise? Yes

34. Precise? No Accurate? Maybe?

35. Accurate? Yes Precise? We cant say!

36. Principles of Measurement

37. Three students measure the room to be 10.2 m, 10.3 m and 10.4 m across. Were they precise? Were they accurate? In terms of measurement

38. The Metric System An easy way to measure

39. how far you have to move on this chart, tells you how far, and which direction to move the decimal place. The box is the base unit, meters, Liters, grams, etc. k h D d c m Converting

40. k h D d c m Conversions • Change 5.6 km to millimeters

41. How many numbers mean anything When we measure something, we can (and do) always estimate between the smallest marks. 1 2 3 4 5 Significant figures (sig figs)

42. The better marks the better we can estimate. Scientist always understand that the last number measured is actually an estimate Significant figures (sig figs) 1 2 3 4 5

43. All nonzero numbers are significant! So….what do we do with zeros?? We follow the rules! Sig Figs

44. Only applied to measured data. Counting numbers are infinitely significant! All nonzero digits are significant! All zeros between nonzero digits are significant! In a decimal number all zeros to the right of the last nonzero digit are significant! Significant Digit Rules

45. In a decimal number all zeros to the left of the first nonzero digit are NOT significant! In a number WITHOUT a decimal all trailing zeros (zeros to the right of the last nonzero digit) are NOT significant! Significant Digit Rules

46. Scientific Notation only shows significant digits in the decimal part of the expression. A decimal point following a zero at the end of the number indicates that the zero is significant. Remember….

47. 50 has only 1 significant figure if it should have two, how can I write it? A decimal following a zero at the end. 50. A line over the significant zero 50 Scientific notation 5.0 x 101 now the zero counts Problems

48. How many sig figs in the following measurements? 458 g 4085 g 4850 g 0.0485 g 0.004085 g 40.004085 g Sig figs.

49. 405.0 g 4050 g 0.450 g 4050.05 g 0.0500060 g Next we learn the rules for calculations Sig Figs.

50. The last sig fig in a measurement is an estimate. Your answer when you add or subtract can not be better than your worst estimate. You must round the answer to the least precise place of the measurement in the problem Adding and Subtracting with Sig Figs