Theme I: What causes things to move, on Earth and in the Heavens?

1. Methods of measuring space and time
   1. Time -- Counting periodic events
   2. Space
      1. Distance between two points & Position with respect to an origin.
      2. Displacement
      3. Velocity
      4. Acceleration
      5. Relationships between Position, Velocity and Acceleration
         1. Graphical methods: x vs t, v vs t, a vs t
            1. slope of v vs t graph gives a
            2. area under v vs t graph gives displacement, change in position
         2. Algebraic formulae for constant acceleration
            1. a = dv/dt
            2. v = a delta-t
            3. delta-x = v_o delta-t + (1/2) a (delta-t)²
            4. a delta-x = (1/2) (vf² - vi²)
      6. Extend these ideas to three dimensions
         1. Vectors (prototype: displacement) as arrows on a map. Have both length and direction .
         2. Vector Properties
            1. Equal vectors: Same length and direction
            2. Adding vectors. Tip to tail
            3. The negative of a vector (reverse direction)
            4. Subtracting vectors (two equivalent methods)
            5. Dealing with vector components in an x,y,z coordiante system
      7. displacement, Velocity and acceleration are vectors, time, distance and speed are not.
2. The "Causes" of motion
   1. Objects keep moving with constant velocity unless something happens.
      Galileo's Law of Inertia or Newton's First Law.
      Defines what we mean by "something happening."
   2. A constant force on something causes acceleration -- constant changes in velocity for equal time intervals
      --Newton's first Law of motion
      1. Verify constant force with a spring between agent and victim
      2. the amount of acceleration depends on the object --
         --this leads to a way of determining "mass": m1/m2 = a2/a1
   3. Two equal forces in same direction on same object cause double acceleration
   4. Two equal forces in opposite directions on same object cancel
   5. If forces are acting on an object in different directions they add like vectors
   6. F = ma summarizes these observations
   7. Does this law work in 3-D as well:
      Experiment says yes, so F = ma
      1. Circular motion: centripetal force F = 4 pi²mr/T² towards centre of circle
      2. Projectile motion, gravity always down F_g = mg
         -- Parabolic trajectory, Horizontal velocity not changing and vertical velocity is cosntantly accelerating.
3. On a spherical earth, a parabolic trajectory becomes an orbit if the object is thrown faster and faster.
4. Newton finds relationship between acceleration of apple on earth and moon far away from the earth's center.
5. Kepler observes relationship between orbital period and radius: Kepler's Law, R³/T² = constant
6. Galileo observes moons of Jupiter and Newton confirms Kepler's Law
7. Result: Universal force law for gravitation true everywhere:
   1. All objects attract each other.
   2. For two objects

      F_gravity = G mM/R²

   3. Forces of m on M and of M on m are equal in magnitude and opposite in direction

Theme II: Conservation Laws

1. Conservation of energy (Mechanical energy conserved in some situations.)
2. Conservation of momentum -- Newtons third laws, Force on a by b = and opposite to force on b by a.
3. These make solving many problems easier
   1. Suicide Pendulum
   2. Roller Coaster
   3. Collisions and explosions

Light

Electrostatics