High School Physics Chapter 1
Math Review for Physics: Algebra
Math Review for Physics: Algebra
Math Review for Physics: Trigonometry
Math Review for Physics: Trigonometry
Quadratic & Inverse Relationships
Quadratic & Inverse Relationships
The Metric System: Units and Conversion
The Metric System: Units and Conversion
liter
The basic unit for volume is the
y = mx + b
We call this the slope-intercept form because here m is the slope, and b is the y-intercept. The slope gives us a measure of the steepness of the curve, and the y-intercept tells us the point where the curve passes through the y-axis of the graph. The last two variables, x and y, are the coordinates for any point on the curve.
If we knew all the side lengths, which inverse trigonometric function could we use to find the angle theta in the following image?
You can use any of the inverse trigonometric functions.
the Kelvin
Zero Kelvins is the lowest possible temperature ever! Zero Kelvins is about -273 degrees Celsius and each Kelvin is the same size as a degree Celsius. So, zero degrees Celsius is equal to about 273 Kelvins.
Pythagorean theorem
a^2 + b^2 = c^2
inverse trigonometric functions
arcsin(opposite / hypotenuse) = theta arccos(adjacent / hypotenuse) = theta arctan(opposite / adjacent) = theta arccsc(hypotenuse / opposite) = theta arcsec(hypotenuse / adjacent) = theta arccot(adjacent / opposite) = theta
Derived units
are created by combining base units using algebra. To see this, let's look at the dimension of volume. Volume measures the amount of 3-D space an object takes up. No matter what shape your object is, we find volume by multiplying three lengths together.
Mass
is how much of something you have, or the amount of matter in an object.
kilogram
is the base unit for mass, represented by the symbol kg. One reason kilograms are a nice unit for students is that, unlike pounds, they're only a measure of mass. Pounds can be used as a name for a mass unit or a weight (i.e., force) unit.
zero rule
states that any number raised to a power of zero is always equal to 1.
Boyle's law
states that at a constant temperature the volume and pressure of a gas are inversely proportional to each other.
equation of a line.
we can represent the curve mathematically using the slope-intercept form of the
inversely proportional relationships
we specify that as one variable increases the other decreases at the same rate. Can be represented by y = k/x
directly proportional relationship
where the variables are increasing or decreasing at the same rate and the curve passes through the origin, (0,0) point, of the graph.
hyperbola
which looks roughly like two parabolas facing back to back on a graph.
Which of the following is the closest to the mass of 500 mL of water?
0.500 kg
What is the density of a solid that has a mass of 9.2 grams and a volume of 12.3 cm^3? Would this object float or sink in water?
0.75 g/cm^3, float
An empty container has a mass of 62.000 grams. You fill it with 24.6 mL of a liquid. The final mass of the container is 81.34 grams. What is the density of the liquid?
0.786 g/mL
meter.
1,000 millimeters in a
What is the mass of a liquid with a density of 2.12 g/mL and a volume of 53.0 mL?
112 g
0 CELCIUS =
273 KELVIN
How many mL are in 3.4 L?
3,400 mL
How many significant figures are in 54,050?
4
If you add 50.0 mL of water to a beaker containing 22 mL of water, how much total water do you have in the beaker?
72 mL
When graphing a linear relationship, what do the data points form?
A straight best fit line
Which is NOT a major branch of physics?
All are correct
Which of the following situations does NOT meet the requirements for a direct relationship?
As one variable increases the other decreases
TF= (9/5) TC + 32
Celsius to Fahrenheit
Elements of the SI: Base & Derived Units
Elements of the SI: Base & Derived Units
The branch of physics known as Mechanics deals with what?
Forces and the behavior of objects
What is SI units shorthand for?
International System of Units
Linear & Direct Relationships
Linear & Direct Relationships
DENSITY=
MASS/VOLUME
Physics-wise, what was significant about the 16th and 17th centuries?
People like Copernicus, Galileo, and Newton had significant scientific breakthroughs
Significant Figures and Scientific Notation
Significant Figures and Scientific Notation
What is a scientific law?
Statements that are considered scientific truths
Which best describes the field of physics?
The study of matter and energy
What is the point of having units in the sciences?
They distinguish our numbers as measurements instead of pure numbers.
Unit Conversion and Dimensional Analysis
Unit Conversion and Dimensional Analysis
Equations/ Derived Units
VOLUME = m X m X m VOLUME = m^3 N = kg m/ s^2 Density = kg/m^3 WAVENUMBER = m^-1 CONCENTRATION = mol/m^3 ENERGY = J = N m = kg m^2/s^2
What is Physics? - Definition, History & Branches
What is Physics? - Definition, History & Branches
When would we want to use the trigonometric functions to find the side lengths of a right triangle?
When we know one side length and one of the angle measurements other than the right angle.
What do we call an SI unit that is created by combining base units using algebra?
a derived unit
polynomial
a math equation with multiple terms. For example, the polynomial a - b has the two terms of 'a' and 'b.'
dimensional analysis and the factor-label method
a simple tool for solving problems not just in chemistry, but in everyday life. It allows us to convert a number from one unit to another unit.
dynamics
a unique field of physics in that it is the study of fluids and their physical properties. Fluids can be liquids or gases
Which of the following is the formula for the Pythagorean Theorem?
a^2 + b^2 = c^2
base units
are the seven most basic units from which all other units are obtained
direct relationship
as one variable increases, the other increases, or as one decreases, the other decreases.
degrees Celsius
boiling point of water is 100 degrees Celsius 30 is hot 20 is nice 10 is cold 0 is ice
In what way are cosecant and sine related to each other?
csc(theta) = 1 / sin(theta)
units
determines the scale of the dimension's measurement. For instance, the dimension of length can have units of inches, yards, miles, and so on. In a science course, you'll see units represented by a symbol after a number.
dimension
determines the type of measurement you are working with. Dimensions include things such as length, volume, time, mass, etc.
negative rule
explains how we can reform a negative exponent as a positive one by writing the number it is being raised to as a reciprocal. In other words, a number raised to a negative power is equal to one divided by that number raised to a positive power of the same magnitude.
power rule
explains that when we have an exponent raised to another exponent this is the same as having the two exponents multiplied together.
density
how tightly packed the particles of an object are
inverse relationship
instead of the two variables moving in the same direction they move in opposite directions, meaning as one variable increases, the other decreases.
What do we use when we know the side lengths of a right triangle but want to find the various angles inside the triangle?
inverse trigonometric functions
quadratic relationship
is a mathematical relation between two variables that follows the form of a quadratic equation. To put it simply, the equation that holds our two variables looks like the following: y =a x ^2 + b x + c
significant figure
is a number that plays a role in the precision of a measurement.
conversion factor
is a relationship in the form of an equality. For example, 7 days/1 week, 60 seconds/1 minute, or 12 inches/1 foot are all examples of conversion factors. Some conversion factors may be difficult to identify. For example, the density of aluminum is 2.7 g/cm^3.
centimeter
is about the width of your pinky. There are exactly 100 centimeters in a meter.
Slope
is defined as rise over run. Rise is the vertical change between two points on a line, and run is the horizontal change between two points on a line.
Mass
is measured using a balance
Scientific notation
is often used in chemistry as a way of representing either very large or very small numbers, and chemists often use very large or very small numbers.
Mechanics
is one major branch of physics, and this focuses on the behavior of objects and the forces that act upon them. Classical mechanics and quantum mechanics are two sub-fields of this branch.
thermodynamics
is one major branch of physics, and this focuses on the behavior of objects and the forces that act upon them. Classical mechanics and quantum mechanics are two sub-fields of this branch.
mole
is the base unit for amount of substance, represented by the symbol mol. When we say a mole is measuring the amount of substance, we are talking about the number of elements, such as molecules, atoms, electrons, etc., in that amount of substance. A mole is equal to 6.023 x 10^23 elements of the substance you are measuring. For example, 1 mole of water contains 6.023 x 10^23 water molecules.
meter
is the base unit for distance, represented by the symbol m. If you've ever seen a meter stick, you already know exactly how long this is. If you're more familiar with yard sticks, it's just slightly longer than that.
amperew
is the base unit for electric current, represented by the symbol A. Electric current is the rate of flow of electricity. It is responsible for powering everything from flashlights to the computer you're watching this on no
candela
is the base unit for luminous intensity, represented by the symbol cd. From the name, you might be able to guess that a standard candle has a luminous intensity of about 1 candela. If you look at a lit candle and a light bulb right next to each other, you'll be able to tell that the light bulb is a much more intense light. The candela is how we represent these different intensities using numbers.
kelvin
is the base unit for temperature, represented by the symbol K. Kelvin is a unique temperature scale because it never goes to negative numbers. Nothing in the universe can be colder than zero kelvin.
second
is the base unit for time, represented by the symbol s. This is the smallest increment on a microwave, or the fastest hand on a clock. It's the tiniest amount of time people deal with on a day-to-day basis.
meter
is the basic unit of length in the metric system
weight
is the force of gravity on an object.
volume
is the measure of how much space it takes up.
kilometer
is the metric version of our mile, even though it's a bit shorter than our mile. A kilometer is equivalent to exactly 1,000 meters.
Electromagnetism
is the study of electrical and magnetic forces, both of which are major components of physics. Without this field of study we wouldn't have electricity to power our homes.
Which of the following is an example of a unit?
meter
Which of the following are arranged from smallest unit to largest unit?
mm, cm, m, km
one rules
much like the zero rule, the number 1 raised to whatever power is always equal to 1.
International System
of Units or SI units for short. SI units consist of an extension of the original metric system and were first put into place during the 11th General Conference on Weights and Measures in 1960. This unit system is fluid and can be updated as needed when new, more precise methods of measurement become available.
parabola
on a graph looks like a dip or a valley.
constant of proportionality.
our slope is a constant, meaning it is a number that never changes. For a directly proportional relationship, we call this the
precision of an instrument
refers to the smallest repeatable digit that the instrument can measure to
product rule
shows us how two equal numbers with different exponents multiplied together is equal to that number raised to the addition of the two exponents.
trigonometric functions.
sin(theta) = opposite / hypotenuse cos(theta) = adjacent / hypotenuse tan(theta) = opposite / adjacent csc(theta) = 1 / sin(theta) = hypotenuse / opposite sec(theta) = 1 / cos(theta) = hypotenuse / adjacent cot(theta) = 1 / tan(theta) = adjacent / opposite
scientific laws
statements describing phenomena that have been repeatedly tested and confirmed
Acoustics
study of sound and waves
distributive law
tells us how to multiply or divide a polynomial by a single number or variable. We do this by the following method. a * (b + c) = ab + ac or (b + c) / a = b/a + c/a
quotient rule
tells us that two equal numbers with different exponents being divided together is equal to that number raised to the subtraction of the two exponents.
gram
the basic unit for mass is the... To give you an idea of the relative size of a gram, the mass of a penny is about 2.5 grams.
linear relationship
the data points form a straight, best-fit line
optics
the study of light and its properties
Physics
the study of matter and energy, is an ancient and broad field of science.
relativity
this branch specifically looks at systems with properties of the Theory of Relativity.
