====== Notes on Khan Academy Physics ======

The original videos made by Salman Khan are wonderful.
The subsequent corrections, additions, and reorganizations made by minions are awful.
As of June 2022 there are several different overlapping course outlines, including:
  * Middle School Physics - NGSS
  * High School Physics
  * High School Physics - NGSS
  * AP/College Physics 1

We chose the one labelled "Physics Library"
https://www.khanacademy.org/science/physics/

===== One-dimensional motion =====
==== Introduction to Physics ====

Biology\\
Chemistry\\
Physics\\
Math\\

Math is a pure mental world.  
Physics applies mathematical models to interactions among objects in the world.
Chemistry applies physics models to the smallest elements.
Biology is based on chemistry.


=== Some basic equations ===

\begin{align}
\vec{F} &= m \vec{a} && \text{force} = \text{mass times acceleration} \\
\vec{d} &= \vec{v} t && \text{displacement} = \text{velocity times time} \\
\vec{a} &= \frac{\Delta\vec{v}}{\Delta t} && \text{acceleration} = \text{change in velocity over change in time}\\
\end{align}

=== Personalities ===

Isaac Newton - classical mechanics \\
Max Planck - the very small \\
Albert Einstein - the very fast, the speed of light

"When you change the way you look at things, the things you look at change."
- Max Planck

==== Displacement, velocity, and time ====

==== Intro to vectors and scalars ====

^ scalar        ^ vector                      ^
| has magnitude | has magnitude and direction |
| speed         | velocity                    |
| distance      | displacement                |  

\begin{align}
s &= d / t && \text{speed = distance / time}\\
s &= 5m / 2s  && \text{move a brick 5 meters in 2 seconds}\\
s &= 2.5 m/s && \text{speed is 2.5 meters per second}\\
\\
\vec{v} &= \vec{d} / t && \text{velocity = displacement / time}\\
\vec{v} &= 5m / 2s  && \text{move a brick 6 meters to the right in 2 seconds}\\
\vec{v} &= 2.5 m/s \text{ to the right}\\
\end{align}

==== Intro to reference frames ====

Point of view from which we measure things.

* ground, stationary
* plane, moving to the right at 250 m/s
* car, moving to the left at 50 m/s


==== Calculating average velocity or speed ====
==== Solving for time ====
==== Displacement from time and velocity example ====
==== Instantaneous speed and velocity ====
==== Position vs time graphs ====

==== notes ====

\begin{align}
|\vec{v}| &= s && \text{magnitude of a vector is the speed} \\
|\vec{d}| &= d && \text{magnitude of a displacement is the distance} \\
\end{align}

Using calculus we see that the area under a velocity-time line is distance.

Slope.

Instantaneous vs average velocity.

==== Acceleration ====


\begin{align}
\vec{a} &= \frac{\Delta v}{\Delta t} && \text{Acceleration = change in velocity over change in time}\\
\vec{a} &= \frac{60 - 0}{3 - 0} && \text{porsche 911 accelerates from 0 to 60 in 3 seconds}\\
\vec{a} &= 20 m/h/s && \text{miles per hour per second}\\
\vec{a} &= \frac{1}{180} m/s^2 && \text{miles per second squared}\\
\end{align}

Displacement per second per second

Acceleration-time line\\
Rise over run\\
The area under the line gives the change in velocity

==== Kinematic formulas and projectile motion ====

==== Old videos on projectile motion ====

\begin{align}
\Delta x &= \text{change in position}\\
t &= \text{time interval}\\
\vec{v}_i &= \text{initial velocity as m/s}\\
\vec{v}_f &= \text{final velocity as m/s}\\
\vec{a} &= \text{constant acceleration in } m/s^2\\
\\
v_f &= v_i + at\\
\Delta x &= v_i t * 1/2 at^2\\
\Delta x &= \frac{v_f + v_i}{2} t\\
v_f^2 &= v_i^2 + 2a\Delta x\\
\end{align}


===== Two-dimensional motion =====

Projectile motion

=== Horizontally launched projectile ===


===== Forces and Newton's laws of motion =====
===== Centripetal force and gravitation =====
===== Work and energy =====
===== Impacts and linear momentum =====
===== Torque and angular momentum =====
===== Oscillations and mechanical waves =====
===== Fluids =====
===== Thermodynamics =====
===== Electric charge, field, and potential =====
===== Circuits =====
===== Magnetic forces, magnetic fields, and Faraday's law =====
===== Electromagnetic waves and interference =====
===== Geometric optics =====
===== Special relativity =====
===== Quantum Physics =====
===== Discoveries and projects =====
===== Review for AP Physics 1 exam =====
===== Cosmology and astronomy =====