===== General Physics =====

====Newton's 3 laws====
  1) objects in motion stay in motion, a body at rest stays at rest, until a force is applied ("law of inertia")
  2) change in momentum of a body is equal in magnitude and direction to the force applied to it (force = mass * acceleration)
  3) when two bodies interact, they apply forces that are equal to each other, and opposite in direction ("law of action and reaction")

Basic definitions:
  * **Force** is in newtons or pounds. One newton = 1kg * m / s² (the force needed to accelerate 1kg at 1 m/s²)
    * f = ma
  * **Momentum** is p
    * p = mv
  * **energy or work** (joules) = force * distance
    * J = F*d = applying 1 newton for 1 meter (units of kg * m²/s²)
    * F = J/d
    * Work is positive if it is applied in the same direction as movement
    * No (net) work is done moving an object horizontally some set distance (unless you overcome friction) - it does not gain or lose potential energy, or have increased kinetic energy at the conclusion
  * **power** = work/time (joules/sec or watts) 

Fnet = Δp / Δt (since p = mv and Δv/Δtime = acceleration)

Change in potential energy is given by U=mgh
  * potential energy: 
    * U = 1/2 kx² (spring), or 
    * P = mgh (at mass at some height, even on an inclined plane)
  * kinetic energy:   K = 1/2 mv²


**dimensional homogeneity** - units must be correct for parts added together, left side matches right side, etc.


====Distance, time, velocity, acceleration====
Displacement is change in position.
  s(t) = s0 + t*(v0+vt)/2
    s = displacement from origin at time t
  vt = v0 + a*t
  if v0 = 0 then
    s(t) = s0 + t²*(a)/2
  so in free-fall, from position 0, you have:
    s(t) = g * t²/2


====Collisions====

  * **elastic**: Two objects bounce off each other.  Kinetic energy, momentum conserved, no other energy created
  * **inelastic** Two objects stick to each other. Momentum conserved, kinetic energy is not conserved (some energy converted to heat, sound, etc.)

**coefficient of restitution** = ratio of energy conserved after collision
    e = (vel. after collision) / (vel. before collision)
     (for collision with immovable object)
    e = (Vfa * Vfb) / (Via * Vib)
     (for collision between objects a and b. f = final, i = initial velocity)
    e = 1 for perfectly elastic, 0 for perfectly inelastic

**conservation of momentum**: p1i + p2i = p1f + p2f
  for m1 having velocity u1 to the right, m2 initially at rest, ends with velocity v2.
    x dimension: m1u1 = m1u2cosθ1 + m2v2cosθ2
    y dimension:   0  = m1u2sinθ1 - m2v2sinθ2

Glancing blow: If and only if both masses are equal (like billiards), then the angle between the resulting vectors is always 90 degrees.

====Inclined plane====
  normal force = force perpendicular to the plane
  normal force on a block resting on a slope, θ = degrees from horizontal:
    f = m*g*cos(θ)
  parallel force = force parallel to the inclined plane
    f = m*g*sin(θ)
  When parallel force > friction, it is unbalanced and objects will move down the plane
  Applied force - friction = net force

====Friction====
Coefficient of friction 
  * μ = f/N  (force applied divided by Normal force)
  * fNet = fApp - Ffriction

  static friction - 
    μS (mu static) = fS/N 
        (fS = force where static friction is overcome
          N = normal force) must be overcome before the mass moves
    μS = fs/N = m*g*sin(θ) / m*g*cos(θ) = sin(θ)/cos(θ) = tan(θ)
  kinetic friction - moving friction
   only one type of friction applies at a time


====Projectile fired at an angle====
  Vx = Vo*cos(θ)
  Vy = Vo*sin(θ) - gt
  x = Vx*t
  y = Vy*t - g*t²/2

projectile follows the shape of a parabola
  y = Ax² + Bx
  y = -gx²/(2(VoCos(θ))²) + xtan(θ)
  time of flight: t = 2Vosin(θ)/g
  max height: H = (Vosin(θ))²/2g
  distance: x = sin(2*θ)*Vo² / g

  Vo = initial velocity
  Can use 2sin(θ)cos(θ) = sin(2θ)
   if filling in t with time of flight in the x = Vx*t formula

Vf² = Vi² + 2ad  ?

====Buoyant force====
pressure P = F/A (force/area)

hydrostatic gauge pressure:  P = pgh, p = density of fluid, g=gravity, h=height (depth)

buoyant force Fb = Fup - Fdown
  Fb = pgVf,  where Vf = volume of displaced fluid, and density * volume = mass, so
  Fb = mf*g,  where mf = mass of displaced fluid
  => buoyant force depends on mass of displaced fluid, not the mass of the object
 
====Gravity====
gravitational constant between two bodies
  F = G * m1 * m2 / r²
  and g = G * m1 / r²
  gE (gravity Earth)  = 9.8 m/s²


====Kinematics====
no use of forces in the equations
  typical equations:
     d = vo*t + 1/2*a*t²
     d = (vo + vf)/2 * t
    vf²= vo² + 2ad
    vf = v0 + at


====Optics====
Refraction on going into a different medium
 
**Snell's law** 
   sin(θ₁) / sin(θ₂) = v₁/v₂ = n₂/n₁  (note that the n values are reversed)
   v = velocity of light in that medium, n = index of refraction
   v = c/n  (c = speed of light in a vacuum)
   it bends towards the normal direction when entering denser material
   (and slows down). bend is because photons are waves.
   
   Critical angle : smallest angle that results in total reflection, no refraction
   θc = arcsin(n₂/n₁)


====Miscellaneous====

IV = independent variable - the variable you control, typically x axis

DV = dependent variable - the variable measured (changes because of the experiment) y axis

FBD = free body diagram - a drawing of mass and all the forces that are applied to it.

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