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--- urp:physgen [2021-10-17]
nerf_herder created
+++ urp:physgen [2021-11-16]
nerf_herder
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-==== General Physics ====
+===== General Physics =====
-  * [[#Newton's 3 laws]]
-  * [[#displacement, time, velocity, acceleration]]
-  * [[#inclined plane]]
-  * [[#Spring]]
-  * [[#Projectile fired at an angle]]
-  * [[#Buoyant force]]
-  * [[#Gravity]]
-  * [[#Kinematics]]
-  * [[#Miscellaneous]]
-===Newton's 3 laws===
+====Newton's 3 laws====
 ) objects in motion stay in motion, a body at rest stays at rest, until a force is applied ("law of inertia")
 ) change in momentum of a body is equal in magnitude and direction to the force applied to it (force = mass * acceleration)
 ) when two bodies interact, they apply forces that are equal to each other, and opposite in direction ("law of action and reaction")
-F=ma
+Basic definitions:
-newton:  1N = 1kg * m / s^2 (the force needed to accelerate 1kg at 1 m/s^2)
+  * 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 = work (joules) = force * distance
+    * J = F*d = applying 1 newton for 1 meter (units of kg * m²/s²)
+    * F = J/d
+  * power = work/time (joules/sec or watts)
-Fulcrum: t = r * f  (torque = radius * force)
+Fnet = Δp / Δt (since p = mv and Δv/Δtime = acceleration)
-just add the torques for multiple objects on one side of a fulcrum
-Momentum is p
+Change in potential energy is given by U=mgh
-  p = mv
+  * potential energy:
-  Fnet = delta p / delta t
+    * U = 1/2 kx² (spring), or
+    * P = mgh (at mass at some height, even on an inclined plane)
+  * kinetic energy:   K = 1/2 mv²
-J = F*d = 1 newton for 1 meter = kg * m^2/s^2
-F=J/d
-energy = work (joules) = force * distance
-kinetic energy = 1/2 * mv^2
-Change in potential energy is given by
+**dimensional homogeneity** - units must be correct for parts added together, left side matches right side, etc.
-U=mgh
-Joule = kg * m^2/s^2
-dimensional homogeneity - units must be correct, 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
-===displacement, time, velocity, acceleration===
- s(t) = s0 + t*(v0+vt)/2
+====Collisions====
-s=displacement from origin at time t
- vt = v0 + a*t
-if v0 = 0 then
- s(t) = s0 + t^2*(a)/2
-so in free-fall, from position 0, you have:
- s(t) = g * t^2/2
+  * **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.)
-==collisions==
+**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
-elastic: two objects bounce off each other
+**conservation of momentum**: p1i + p2i = p1f + p2f
-   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.)
-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 both masses are equal (like billiards):
+Glancing blow: If and only if both masses are equal (like billiards), then the angle between the resulting vectors is always 90 degrees.
-  angle between the resulting vectors is always 90 degrees
+====Inclined plane====
-===Inclined plane===
   normal force = force perpendicular to the plane
-  normal force on a block resting on a slope:
+  normal force on a block resting on a slope, θ = degrees from horizontal:
-  f = m*g*cos(degrees from horizontal)
+    f = m*g*cos(θ)
   parallel force = force parallel to the inclined plane
-   it is unbalanced (objects will move down the plane), sometimes called net force
+    f = m*g*sin(θ)
-  f = m*g*sin(theta)
+  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 -
-    uS (mu static) = fS/N
+    μS (mu static) = fS/N
         (fS = force where static friction is overcome
           N = normal force) must be overcome before the mass moves
-    uS = fs/N = m*g*sin(theta) / m*g*cos(theta) = sin(theta)/cos(theta) = tan(theta)
+    μS = fs/N = m*g*sin(θ) / m*g*cos(θ) = sin(θ)/cos(θ) = tan(θ)
-  kinetic friction - normal moving friction
+  kinetic friction - moving friction
    only one type of friction applies at a time
-==Spring==
-Hooke's law: F=-kx, k=spring constant, x = displacement
-===Projectile fired at an angle===
+====Projectile fired at an angle====
- Vx = Vo*cos(theta)
+  Vx = Vo*cos(θ)
- Vy = Vo*sin(theta) - gt
+  Vy = Vo*sin(θ) - gt
- x = Vx*t
+  x = Vx*t
- y = Vy*t - (1/2)*g*t^2
+  y = Vy*t - g*t²/2
 projectile follows the shape of a parabola
- y = Ax^2 + Bx
+  y = Ax² + Bx
- y = -gx^2/(2(VoCos(theta))^2) + xtan(theta)
+  y = -gx²/(2(VoCos(θ))²) + xtan(θ)
-time of flight:
+  time of flight: t = 2Vosin(θ)/g
- t = 2Vosin(theta)/g
+  max height: H = (Vosin(θ))²/2g
-max height:
+  distance: x = sin(2*θ)*Vo² / g
- H = (Vosin(theta))^2/2g
-distance:
- x = sin(2*theta)*Vo^2 / g
- Vo = initial velocity
+  Vo = initial velocity
- They use 2sin(theta)cos(theta) = sin(2theta)
+  Can use 2sin(θ)cos(θ) = sin(2θ)
    if filling in t with time of flight in the x = Vx*t formula
-Vf^2 = Vi^2 + 2ad  ?
+Vf² = Vi² + 2ad  ?
-===Buoyant force===
+====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
+  => buoyant force depends on mass of displaced fluid, not the mass of the object
-===Gravity===
+====Gravity====
 gravitational constant between two bodies
-F = G * m1 * m2 / r^2
+  F = G * m1 * m2 / r²
-  and g = G * m1 / r^2
+  and g = G * m1 / r²
-  gE (gravity Earth)  = 9.8 m/s^2
+  gE (gravity Earth)  = 9.8 m/s²
-===Kinematics===
+====Kinematics====
 no use of forces in the equations
   typical equations:
-     d = vo*t + 1/2*a*t^2
+     d = vo*t + 1/2*a*t²
      d = (vo + vf)/2 * t
-  vf^2 = vo^2 + 2ad
+    vf²= vo² + 2ad
     vf = v0 + at
- 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
-===Miscellaneous===
+====Optics====
-IV = independent variable
+Refraction on going into a different medium
-     - the variable you control, typically x axis
-DV = dependent variable
+**Snell's law**
-     - the variable measured (changes because of the experiment) y axis
+   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
-potential energy: U = 1/2 kx^2 (spring), or P = mgh (at mass at some height)
+DV = dependent variable - the variable measured (changes because of the experiment) y axis
-  (P = m*h*g even on an inclined plane)
-kinetic energy:   K = 1/2 mv^2
+FBD = free body diagram - a drawing of mass and all the forces that are applied to it.
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