Math/Physics

• SI units


  • Meters, kilograms, and seconds (MKS)
  • Centimeters, grams, and seconds (CGS)
  • Length
  • Mass (not weight)
  • Time
  • Current
  • Amount of Substance
  • Temperature
  • Luminous Intensity
• Ångström


  Unit of length, 1 Å = 10^-10 m
• Nanometer


  Unit of length, 1 nm = 10^-9 m
• Electron-volt


  Unit of energy, 1 eV = 1.6 × 10^-19 J
• Vectors


  Numbers that have magnitude and direction
• Scalars


  Numbers that have magnitude only and no direction
• Vectors include displacement, velocity, acceleration, and force
• Scalars include distance, speed, energy, pressure, and mass
• The difference between a vector and scalar quantity can be quite pronounced when there is a nonlinear path involved
• The Earth travels a distance of roughly 940 million kilometers in a year, but its displacement is zero kilometers
• Vector representation


  Arrows, where the direction of the arrow indicates the direction of the vector and the length is proportional to the magnitude
• Resultant


  The sum or difference of two or more vectors
• Tip-to-tail method of vector addition

  1. Place the tail of vector B at the tip of vector A

  2. The lengths of the arrows must be proportional to the magnitudes of the vectors

  3. The vector sum A + B is the vector joining the tail of A to the tip of B and pointing toward the tip of B
• Finding the x- and y-components of a vector

  1. Draw a right triangle with the vector as the hypotenuse

  2. If θ is the angle between the vector and the x-component, then X = |V| cos θ and Y = |V| sin θ

  
• Finding the resultant vector using components

  1. Resolve the vectors into their x- and y-components

  2. Add the x-components to get the x-component of the resultant

  3. Add the y-components to get the y-component of the resultant

  4. Find the magnitude and direction of the resultant using the Pythagorean theorem and inverse trigonometric functions
• Multiplying a vector by a scalar


  Changes the magnitude, with the direction being either parallel or antiparallel to the original direction
• Dot product


  Multiplying the magnitudes of two vectors and the cosine of the angle between them, resulting in a scalar quantity
• Cross product


  Multiplying the magnitudes of two vectors and the sine of the angle between them, resulting in a vector quantity
• Right-hand rule for cross products

  1. Point thumb in direction of first vector

  2. Extend fingers in direction of second vector

  3. Palm points in direction of resultant vector
• A × B ≠ B × A
• Displacement


  Vector that connects the object's initial position and its final position, does not account for the actual pathway taken
• Distance


  Scalar quantity that considers the pathway taken
• Displacement of a person who walks 2 km east, then 2 km north, then 2 km west, and then 2 km south

  • Displacement is zero because the person ends up back at the start
• Velocity


  Vector quantity, magnitude is the rate of change of displacement in a given unit of time
• Speed


  Scalar quantity, the rate of actual distance traveled in a given unit of time
• Instantaneous speed


  Always equal to the magnitude of the object's instantaneous velocity
• Average speed


  Not necessarily equal to the magnitude of the average velocity
• The average speed of the Earth over a year is about 30 kilometers per second, its average velocity is zero
• Force


  Vector quantity experienced as pushing or pulling on objects
• Gravity


  Attractive force felt by all forms of matter, decreases with height above the Earth and increases closer to the Earth's center of mass
• Static friction


  Exists between a stationary object and the surface upon which it rests, 0 <= fs <= μs * N
• Kinetic friction


  Exists between a sliding object and the surface over which the object slides, fk = μk * N
• The coefficient of static friction will always be larger than the coefficient of kinetic friction
• Mass


  Measure of a body's inertia, scalar quantity
• Weight


  Measure of gravitational force on an object's mass, vector quantity
• Center of mass


  Point within an object where the object's weight can be considered to act
• Acceleration


  Rate of change of velocity, vector quantity
• On a velocity vs time graph, the slope indicates the instantaneous acceleration
• Deceleration


  Motion in the direction opposite the initial velocity
• Average acceleration


  Defined as (change in velocity) / (change in time)