Essential Physics

Mathematics connections
Chapter 1 - Science of Physics
Comparing math in an algebra class to math in physics Contrapositive logical statements Digital cameras, additive primary colors, and 256³ colors Hexadecimal RGB colors for web pages Intersecting science, technology, engineering and mathematics Language of mathematics Logical reasoning and statements Mathematical language in physics
Chapter 2 - Physical Quantities and Measurement
Algebra Converting units of time Decimal places Density Dimensional analysis Four-step method for solving problems Graphing quantities using two dimensions (x and y) How to calculate density Linear and non-linear relationships Mathematics of converting units Models and equations Models in mathematics and physics Prefixes in the metric system Scientific notation Setting up word problems Significant figures Significant figures when multiplying and dividing Solving algebraic equations Space is measured in units of length Surface area and volume Using algebra to solve problems Using scientific notation on a calculator Visualizing data
Chapter 3 - Position and Velocity
Assigning variables in order to solve a problem Canceling units in solving problems Choosing an origin for a reference frame Connecting verbal description with graph of motion Difference between speed and velocity Distance is the area under a velocity vs. time graph Equations and unknown quantities Equations using average vs. instantaneous velocity Graphical definition of speed on a position versus time plot Instantaneous velocity is the tangent to a curve on a position-time graph Instantaneous velocity on position vs. time graphs Modeling motion Slope of a graph and its application in physics Solving equations requires using consistent units Solving multiple equations with multiple unknowns Technique for solving physics problems Using mathematics to solve physics problems Velocity is a vector quantity while speed is a scalar quantity “Head-to-tail method” to add vectors
Chapter 4 - Acceleration
Acceleration is the change in velocity over change in time Comparing velocity model to equation for a straight line Graphical models for motion with constant acceleration Particle model for motion Quadratic equations Quadratic equations Using area under the position vs. time graph to derive its mathematical expression
Chapter 5 - Forces and Newton’s Laws
Center of mass Converting units for force Opposing force has negative sign
Chapter 6 - Motion in Two and Three Dimensions
Adding and subtracting vectors using components Adding vectors graphically “head-to-tail” Arrow symbols to denote vector quantities into and out of the page Components of a vector Equations for vector components Force components for an inclined plane Inverse tangent to solve for a vector's position angle Logical operators Magnitude of a vector Mathematical representation of vectors Particle model for motion on Galileo's ramps Particle model for projectile motion Polar coordinates, Cartesian coordinates, and vector diagrams Polar representation of vectors Pythagorean theorem Radians and degrees Ramp coordinates Solving quadratic equation of motion Subscripts in the equations of projectile motion Trigonometric functions Vector model for displacement Vector multiplication Vectors
Chapter 7 - Circular Motion
Measuring angles in radians Radius and the circumference of a circle Relationship between angular speed and linear speed Tangential and radial vectors
Chapter 8 - Static Equilibrium and Torque
Expanding vector notation for summing forces into three directions Exploiting symmetry in equilibrium problems Mathematical notation of Σ for expressing summation
Chapter 9 - Work and Energy
Choosing origin for potential energy reference frame Deducing a physical equation Different rates of change Example of a non-linear relationship Hooke’s Law for springs Nonlinear relationships Proportional relationships
Chapter 10 - Conservation of Energy
Graphical model of a falling wood ball Using algebra to solve conservation of energy problems
Chapter 11 - Momentum and Collisions
Adding vectors in 1D
Chapter 12 - Machines
Gear ratios
Chapter 13 - Angular Momentum
Comparing quantities and equations of motion for translational and rotational motion Downhill rolling velocity depends on the distribution of mass, not mass itself Moment of inertia of a point mass Moments of inertia for various geometrical shapes Precession Proportional relationships in moments of inertia Rolling down an inclined plane
Chapter 14 - Harmonic Motion
Amplitude of an oscillation Frequency of oscillation Period of oscillation Potential energy well graph and stability Stable and unstable equilibria
Chapter 15 - Waves
Constructive interference of waves Destructive interference of waves Energy of a wave and its relationship with frequency Energy of waves and its relationship with frequency Perpendicular and parallel oscillations for waves Perpendicular and parallel oscillations for waves Speed of a wave and how it relates to frequency and wavelength The sine function describes wave motion
Chapter 16 - Sound
Decibel scale for sound is a logarithmic scale
Chapter 17 - Electricity and Circuits
Meaning of proportional and inversely proportional
Chapter 18 - Electric and Magnetic Fields
Force that falls off faster than an inverse square relation Inverse square law: electric force
Chapter 19 - Electromagnetism
Determining the cyclotron radius for ions in a mass spectrometer Right-hand rule for magnetic field around current-carrying wire Tangent of a circle Trigonometric functions are dimensionless
Chapter 20 - Light and Reflection
A normal is a perpendicular line Locating an image with a ray diagram Parallax Ray tracing locates images formed by spherical mirrors Using a compass to locate mirror images
Chapter 21 - Refraction and Lenses
Objects located at “infinity” and reciprocal quantities Ray tracing for thin lenses Sign conventions for lenses Sines of angles in Snell’s law
Chapter 22 - Electromagnetic Radiation
Maxima of the double slit interference pattern for light Minima and maxima in single slit diffraction Orders of magnitude Polarization for transverse waves
Chapter 23 - Properties of Matter
Converting units and understanding energy content from food Maxwellian distribution function for statistical mechanics Using algebra to convert between degrees Fahrenheit and degrees Celsius
Chapter 24 - Heat Transfer
Exponential decay in Newton's law of cooling Proportional reasoning and the heat conduction equation Proportional reasoning for a variable raised to the fourth power
Chapter 25 - Thermodynamics
Calculating the efficiency of a heat engine Calculating work done as the area enclosed on a temperature-entropy graph Permutations and factorials in calculating the entropy of a system
Chapter 26 - Quantum Physics and the Atom
Circular resonance waves
Chapter 27 - Nuclear Physics
Chain reactions Half-life and exponential decay Mass of the proton Mathematics of radioactive decay Solving Einstein's equation Solving the decay rate equation