PHYSICS MATH REVIEW Aw yeah math.

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

Know your symbols! Variables have superscripts and subscripts Variables have superscripts and subscripts i.e: v i 2 i.e: v i 2 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. “v 1 ” means “velocity of 1 st object”) 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. “v 1 ” means “velocity of 1 st object”) superscript – (super = higher ↑) Will denote an exponent. subscript – (sub = below ↓) Used to modify the variable.

Know your symbols! ∆ = DELTA ∆ = 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” In front of a variable it means “change in” i.e. ∆t = “change in time”i.e. ∆t = “change in time” To find ∆, just subtract the initial from the final. To find ∆, just subtract the initial from the final. i.e. ∆v = v f – v i (“change in velocity = v final – v initial”)i.e. ∆v = v f – v i (“change in velocity = v final – v initial”)

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

Know your UNITS Some common units in physics: 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)

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). 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.) Try to have an idea of what reasonable units are for a given situation. (You wouldn’t measure a table in miles.)

Scientific Notation Used to denote numbers with excess leading/trailing zeros. Used to denote numbers with excess leading/trailing zeros = 3.5 x = 3.5 x ,630,000 = 7.63 x 10 67,630,000 = 7.63 x 10 6 Always have only 1 digit before the decimal.Always have only 1 digit before the decimal. Adjust the decimal place to the right or left accordingly.Adjust the decimal place to the right or left accordingly.

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

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

Solving for Variables Examples: Examples: 3b 2 +6 = 18 3b 2 = 18 – 6 = 12 b 2 = 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 – v i ) / 12 = 7 (36 – v i ) = 7 * 12 = 84 – v i = 72 – 36 = 48 v i = -48 v i = -48

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. 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: F=ma (solve for a), a = F/m Ex: volume = l*h*w (solve for w), w = v/(l*h) Ex: volume = l*h*w (solve for w), w = v/(l*h)

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

Calculating Variables Ex: An arrow flies by with a speed of 3.6 m/s. How long does it take to travel 40 cm? 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

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

MATH PRACTICE Complete these problems in your notebook. Work on your own or in small groups. Write the following in Scientific Notation ,000,000 Solve for the variable

Metric Conversion kilo- (k-) thousand 1000 x base hecto- (h-) hundred 100 x base deka- (da-) ten10 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-) millionth1 x 10^-6 x base nano- (n-) billionth1 x 10^-9 x base 3600 seconds = 1 hour

Conversion review Convert 360 km/hr to m/s

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.

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: ?

Conversion review Convert 36 km/hr to m/s

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

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?

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