Physics Math Review

1. Physics Math Review

2. Review Key concepts from other science courses will be used throughout Physics. Examples: Sig Figs Metric System Unit Analysis Trigonometry

3. Metric System The Metric system is the international system of units used in all sciences. The metric system is based on powers of 10 and uses prefixes to indicate the appropriate power of 10 or the # of one unit compared to another.

4. Metric System Prefixes Exponent Meaning Giga (G) 109 One Billion Mega (M) 106 One Million Kilo (k) 103 One Thousand Hecta (h) 102 One Hundred Deka (dk) 101 One Ten Base 100 (1) One

5. Metric System Prefixes Exponent Meaning Base 10o One Deci (d) 10-1 One Tenth Centi (c) 10-2 One Hundredth Milli (m) 10-3 One Thousandth Micro (μ) 10-6 One Millionth Nano (n) 10-9 One Billionth

6. Metric Conversions To convert from one metric unit to another, you multiply or divide by a power of 10 dependent on how far apart the two units are. Ex. 1 km = ?m 1 x 103= 1000m

7. Metric Conversions Another way to accomplish this is to move the decimal place dependent on how far apart the two units are. Ex. 1m = ?km km is located 3 powers to the left of m so move decimal place 3 places left 1m = 0.001km

8. Review Practice 1. 12kL = ___________ L 5. 0.00084nm= _________Mm (use sci. notation) 2. 6200 μm = ________ m 6. 784g = ____________cg 3. 0.00106L = _______hL 7. 0.084kg = _________g 4. 784mg = _________cg 8. 80kg = __________ cg

9. Significant Figures (SIG FIGS) Significant Figures are indicated based on the precision your equipment provides. Final calculations should have a final # of digits based on the “worst” piece of equipment used. Remember that “worst” means fewest # of digits and that when measuring, one digit is always estimated.

10. Sig Fig Rules 1. All non-zero digits are significant 2. Zeroes between non-zeroes are significant 3. Zeroes after a non-zero and after a decimal place are significant 4. Zeroes before non-zeroes are NOT significant

11. Sig Fig Rules (contd.) 5. Zeroes after non-zeroes but before the decimal place are NOT significant. 6. Once you have located the first significant digit, count all digits until you come to a non-significant digit. The # counted is the correct # of sig figs. 7. When multiplying/dividing, the answer will have the same number of sig figs as the # with the least amount of sig figs. 8. When adding/subtracting, the answer will have the same number of decimal places as the # with the fewest decimal places.

12. Sig Fig Practice # of sig figs: 1. 0.0251 kg = ____________________ 2. 10.089 kg = ____________________ 3. 100 cars = _____________________ 4. 0.010 s = ______________________

13. Sig Fig Practice (contd.) Answer with correct # of sig figs: 5. (10.18m)(0.00740m) = ______________ 6. 701g + 4.24g + 57.397g = ___________ 7. (3.4617 x 107) ÷ (5.61 x 10-4)= ________ 8. 9.66kg – 0.25692kg = _______________

14. Scientific Notation Scientific notation differs from standard notation and is used to show very large or very small values. The values are equal to each other, just indicated in different formats.

15. Scientific Notation Instead of writing out an entire number, it is converted to a number between 1 and 9.9 and given an exponent to show the true value. Ex. 9060000 = 9.06 x 106 Ex. 0.0000000417 = 4.2 x 10-8 On calculators, a E notation may be used. Practice with your calculator so you are comfortable with the E notation.

16. Scientific Notation Practice Convert to scientific notation: Convert to scientific notation: 1. 255130000000m = ____________ 5. 1.72 x 10-3hrs ___________ 2. 0.0004572 L =_______________ 6. -4.25 x 10-4 _____________ 3. 77.9cL ____________________ 7. 5.96 x 104 K _____________ 4. -0.0000084kg = ______________ 8. 3.19 x 106 g _____________

17. Unit Analysis • Unit Analysis is a system in which different units are converted. • Equivalent values are used and then units are canceled, leaving you with only the appropriate unit(s) at the end of the conversion. • These units are canceled by dividing by themselves (x/x = 1 so it is “canceled).

18. Unit Analysis Ex. How many seconds are in the school day (8 hours)? 8 hours x 60 minutes x 60 seconds = 28800 seconds 1 hour 1 minute Hours/hours and minutes/minutes are canceled leaving you with seconds as the only unit. In Physics, it is imperative you understand the canceling of units in order to provide correct final units.

19. Unit Analysis Practice 1. Convert your age to seconds (ignore leap years). 2. Convert your height in inches to nm(given 1in. = 2.54cm) 3. Convert 340miles/hr to m/s (1 mile = 5280 feet) 4. How many dabs of peanut butter does it take to make enough peanut butter and jelly sandwiches to feed 4 hungry six year olds if it takes 2.5 sandwiches to feed one child? One PBJ sandwich requires 4 smears of peanut butter, 11 dollops equals 2 smears and 3 dabs are equivalent to 2 dollops. 5. Convert 5.93 cm3 to m3.

20. Unit Analysis Practice Solution

21. Algebra Review Algebra involves the rearranging of values or the transposing of unknowns in an equation. Opposite operations are used to move around parts of the equation. Ex. V = d/t so t = d/V

22. Algebra Review 1. Given F = ma, solve for m. 2. Given I = V/R, solve for R. 3. Given KE = ½ mv2, solve for m. 4. Given KE = ½ mv2, solve for v. 5. Given W = Fdcosθ, solve for θ.

23. Algebra Review Solution

24. Trigonometry Review Basic trigonometry involving triangles and angles will be used throughout physics. The general right triangle as well as the Pythagorean Theorem will be used.

25. Trigonometry Review Right Triangle: SOHCAHTOA Sin θ =opposite Cos θ = adjacent Tan θ = opposite Hypotenuse hypotenuse adjacent Pythagorean Theorem: A2 + B2 = C2 Law of Cosines: R2 = A2 + B2 – 2ABcosθ.

26. Trigonometry Review Solutions