PHYSICS MATH REVIEW

1. PHYSICS MATH REVIEW Aw yeah math. MATHMATICAL!

2. Know your symbols! • v, a, t, d, etc. – VARIABLES • in algebra they can stand for anything • in PHYSICS they only stand for a specific type of quantity! • v = velocity, a = acceleration, t = time, d = distance, F = force, and so on…

3. Know your symbols! • Variables have superscripts and subscripts • i.e: vi2 • The subscripts will stand for a term (“i” means “initial”, “f” means “final”). Or they are used to keep track of which value you’re referencing. (i.e. “v1” means “velocity of 1st object”) superscript – (super = higher ↑) Will denote an exponent. subscript – (sub = below ↓) Used to modify the variable.

4. Know your symbols! • ∆ = DELTA - You might recognize this from chemistry! - It’s the greek symbol for the letter “D” • In front of a variable it means “change in” • i.e. ∆t = “change in time” • To find ∆, just subtract the initial from the final. • i.e. ∆v = vf – vi (“change in velocity = v final – v initial”)

5. Know your UNITS • Every variable in physics will have units attached to it. • For calculations, the units should always be the same • i.e. You can’t subtract 60 seconds from 3 hours directly. You have to give them the same units!

6. Know your UNITS • Some common units in physics: C = Celsius (used for temperature) m = meters (standard unit of length) s = seconds (standard unit of time) kg = kilogram (standard unit of mass) N = Newton (standard unit of force) J = Joule (standard unit of energy)

7. Know your UNITS • Physics uses the metric system (meters, Celsius, grams) but you should be aware of common English units as well (feet, miles, pounds). • Try to have an idea of what reasonable units are for a given situation. (You wouldn’t measure a table in miles.)

8. Scientific Notation • Used to denote numbers with excess leading/trailing zeros. • .00035 = 3.5 x 10-4 • 7,630,000 = 7.63 x 106 • Always have only 1 digit before the decimal. • Adjust the decimal place to the right or left accordingly.

9. Solving for Variables • Order of operations! • PEDMAS: (),2,/,•, +, - • Remember that if two variables are added or subtracted over a denominator, they are treated as if they are in parenthesis. i.e. (a= (vf-vi)/∆t )

10. Solving for Variables • Know the inverse of each operation - (+ vs -), (• vs / ), (2 vs √ ) • Isolate the desired variable through reverse order of operations

11. Solving for Variables • Examples: 3b2+6 = 18 3b2 = 18 – 6 = 12 b2 = 12/3 = 4 b = √(4) = 2 b = 2 Remember that if parentheses are involved, you must deal with everything outside of the parenthesis first. (inverse order of operations) (36 – vi) / 12 = 7 (36 – vi) = 7 * 12 = 84 – vi = 72 – 36 = 48 vi = -48

12. Solving for Variables • Sometimes you’ll have to isolate a variable, even though there are other variables in the equation. Just treat them the same as other numbers, and follow the same procedure. • Ex: F=ma (solve for a), a = F/m • Ex: volume = l*h*w (solve for w), w = v/(l*h)

13. Calculating Variables • First, find the equation dealing with your variable • Next, substitute the given variables with their numbers • Make sure all units are the same • Solve the single variable equation!

14. Calculating Variables • Ex: An arrow flies by with a speed of 3.6 m/s. How long does it take to travel 40 cm? Step 1: Looking for time and we know distance and speed. v = d/t Step 2: Plug in the values (3.6 m/s) = (40cm) / t Step 3: Make the units match 40 cm = .4 meters Step 4: Solve the equation 3.6 = .4/t 1/t = (3.6)/.4 = 9 t = .11 seconds

15. Things to Remember • In physics, answers should be given in decimal form (no fractions). • Decimals should be kept to correct amount of significant figures

16. MATH PRACTICEComplete these problems in your notebook. Work on your own or in small groups. Solve for the variable • Write the following in Scientific Notation • 0.07882 • 118000 • 0.00002786 • 4. 382,000,000

17. Metric Conversion • kilo- (k-) thousand 1000 x base • hecto- (h-) hundred 100 x base • deka- (da-) ten 10 x base • Base (meters, grams, liters) • deci- (d-) tenth .1 x base • centi- (c-) hundredth .01 x base • milli- (m-) thousandth .001 x base • micro- (µ-) millionth 1 x 10^-6 x base • nano- (n-) billionth 1 x 10^-9 x base 3600 seconds = 1 hour

18. Conversion review • Convert 360 km/hr to m/s

19. Challenge Question • A bear is charging with a velocity of 36 km/hr. If it maintains that velocity for 30 seconds, how many meters does it travel? Tips: 1) Find the right equation on your STAAR chart. Write it down. (Hint: It will have time and distance as variables) 2) Plug in the appropriate values 3) Make sure the units are the same (km/hr to m/s) 4) Once all of the above is done, then try and solve the equation.

20. Answer • A bear is charging with a velocity of 36 km/hr. If it maintains that velocity for 30 seconds, how many meters can it travel? • Formula: v=d/t • Values: 36 km/hr = d / 30s • Units: ?

21. Conversion review • Convert 36 km/hr to m/s

22. Answer • A bear is charging with a velocity of 36 km/hr. If it maintains that velocity for 30 seconds, how many meters can it travel? • Formula: v=d/t • Values: 36 km/hr = d / 30s • Units: 36 km/hr = 10 m/s • Solve for d: d = (10m/s)*(30s) = 300 meters

23. Question #1 A linebacker has a mass of 150 kg. If he hits the receiver with a force of 675 kg*m/s^2 (Newtons). What was his acceleration?

24. Answer #1 • A linebacker has a mass of 150 kg. If he hits the receiver with a force of 675 kg*m/s^2 (Newtons). What was his acceleration? Formula: F = ma Values: 675 N = 150kg * a Units already match (kg & kg) Solve for a: a= 675N/150 kg = 4.5 m/s^2