PHYSICS MATH REVIEWPHYSICS MATH REVIEW

Aw yeah math.Aw yeah math.

Know your symbols!Know your symbols!

v, a, t, d, etc. – VARIABLESv, a, t, d, etc. – VARIABLES• in algebra they can stand for anythingin algebra they can stand for anything• in PHYSICS they only stand for a in PHYSICS they only stand for a

specific type of quantity! specific type of quantity!• v = velocity, a = acceleration, t = time, v = velocity, a = acceleration, t = time,

d = distance, F = force, and so d = distance, F = force, and so on…on…

Know your symbols!Know your symbols!

Variables have superscripts and subscriptsVariables have superscripts and subscripts

i.e: i.e: vvii22

The subscripts will stand for a term (“i” means The subscripts will stand for a term (“i” means “initial”, “f” means “final”). Or they are used to keep “initial”, “f” means “final”). Or they are used to keep track of which value you’re referencing. (i.e. “vtrack of which value you’re referencing. (i.e. “v11” ”

means “velocity of 1means “velocity of 1stst object”) object”)

superscript – (super = higher ↑) Will denote an exponent.

subscript – (sub = below ↓) Used to modify the variable.

Know your symbols!Know your symbols!

∆ ∆ = DELTA= DELTA- You might recognize this from chemistry!- You might recognize this from chemistry!

- It’s the greek symbol for the letter “D”- 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 = vi.e. ∆v = vff – v – vii (“change in velocity = v final – v initial”) (“change in velocity = v final – v initial”)

Know your UNITSKnow your UNITS

Every variable in physics will have units Every variable in physics will have units attached to it.attached to it.

For calculations, the units should always For calculations, the units should always be the samebe the same• i.e. You can’t subtract 60 seconds from 3 i.e. You can’t subtract 60 seconds from 3

hours directly. You have to give them the hours directly. You have to give them the same units!same units!

Know your UNITSKnow your UNITS

Some common units in physics:Some common units in physics:

C = Celsius (used for temperature)C = Celsius (used for temperature)

m = meters (standard unit of length)m = meters (standard unit of length)

s = seconds (standard unit of time)s = seconds (standard unit of time)

kg = kilogram (standard unit of mass)kg = kilogram (standard unit of mass)

N = Newton (standard unit of force)N = Newton (standard unit of force)

J = Joule (standard unit of energy)J = Joule (standard unit of energy)

Know your UNITSKnow your UNITS

Physics uses the metric system (meters, Physics uses the metric system (meters, Celsius, grams) but you should be aware Celsius, grams) but you should be aware of common English units as well (feet, of common English units as well (feet, miles, pounds).miles, pounds).

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

Scientific NotationScientific Notation

Used to denote numbers with excess Used to denote numbers with excess leading/trailing zeros.leading/trailing zeros.• .00035 = 3.5 x 10.00035 = 3.5 x 10-4-4

• 7,630,000 = 7.63 x 107,630,000 = 7.63 x 1066

• 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 Adjust the decimal place to the right or left

accordingly.accordingly.

Solving for VariablesSolving for Variables

Order of operations!Order of operations! PEDMAS: (),PEDMAS: (),22,/,,/,•, +, -•, +, -

Remember that if two variables are added Remember that if two variables are added or subtracted over a denominator, they are or subtracted over a denominator, they are treated as if they are in parenthesis. treated as if they are in parenthesis.

i.e. (a= (vi.e. (a= (vff-v-vii)/∆t ) )/∆t )

Solving for VariablesSolving for Variables

Know the inverse of each operationKnow the inverse of each operation

- (+ vs -), (- (+ vs -), (• vs / ), (• vs / ), (2 2 vs √ )vs √ )

Isolate the desired variable through Isolate the desired variable through reverse order of operationsreverse order of operations

Solving for VariablesSolving for Variables

Examples:Examples:3b3b22+6 = 18+6 = 18

3b3b22 = 18 – 6 = 12 = 18 – 6 = 12

bb22 = 12/3 = 4 = 12/3 = 4

b = b = √(4) = 2√(4) = 2

b = 2b = 2

Remember that if parentheses are involved, you must Remember that if parentheses are involved, you must deal with everything outside of the parenthesis first. deal with everything outside of the parenthesis first. (inverse order of operations)(inverse order of operations)

(36 – v(36 – vii) / 12 = 7) / 12 = 7

(36 – v(36 – vii) = 7 * 12 = 84) = 7 * 12 = 84

– – vvii = 72 – 36 = 48 = 72 – 36 = 48

vvii = -48 = -48

Solving for Variables Solving for Variables

Sometimes you’ll have to isolate a Sometimes you’ll have to isolate a variable, even though there are other variable, even though there are other variables in the equation. Just treat them variables in the equation. Just treat them the same as other numbers, and follow the the same as other numbers, and follow the same procedure.same procedure.

Ex: F=ma (solve for a), a = F/mEx: 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 VariablesCalculating Variables

First, find the equation dealing with your variableFirst, find the equation dealing with your variable Next, substitute the given variables with their Next, substitute the given variables with their

numbersnumbers Make sure all units are the sameMake sure all units are the same Solve the single variable equation!Solve the single variable equation!

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

travel 40 cm?travel 40 cm?

Step 1: Looking for time and we know distance and speed. Step 1: Looking for time and we know distance and speed. v = d/tv = d/t

Step 2: Plug in the valuesStep 2: Plug in the values(3.6 m/s) = (40cm) / t(3.6 m/s) = (40cm) / t

Step 3: Make the units matchStep 3: Make the units match40 cm = .4 meters40 cm = .4 meters

Step 4: Solve the equationStep 4: Solve the equation3.6 = .4/t3.6 = .4/t1/t = (3.6)/.4 = 91/t = (3.6)/.4 = 9t = .11 secondst = .11 seconds

Things to RememberThings to Remember

In physics, answers should be given in In physics, answers should be given in decimal form (no fractions). decimal form (no fractions).

Decimals should be kept to correct amount Decimals should be kept to correct amount of significant figuresof significant figures

MATH PRACTICEComplete these problems in your notebook. Work on your own or in

small groups.

4.0)4(2

1

219

83

9

2)5(2

84)9(7

3178

k

m

v

n

k

n Write the following in Scientific Notation

• 0.07882

2. 118000

3. 0.00002786

4. 382,000,000

Solve for the variable

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

Conversion review

• Convert 360 km/hr to m/s

sm

ss

hr

hr

hrm

mmkm

km

/100

1003600

1360000

/360000

36000010001

360

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 values3) 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

mmkm

km360001000

1

36

hrm /36000

ss

hr

hr10

3600

136000

sm /10

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