Lecture 4: Understanding Motion, Energy, and Gravity: Physics in a Word

3. How do we describe motion?
   1. deceleration: The term usually means an acceleration opposite the direction of motion.
5. The acceleration of gravity near the Earth's surface.
   1. Earth's gravitational field strength g = 9.8 N/kg = 9.8 m/s**2 (fiducial value).
   2. File: Gravity file: gravity_acceleration_little_g.html.
6. The acceleration of gravity.
   1. A bit of mathematical physics:

        Law of gravity F_g = mg = ma = F_net_force Newton's 2nd law of motion
                             mg = ma 
                              g = a 
                          v = gt = at
                          d=(1/2)gt**2=(1/2)at**2 

   2. Galileo's "falling bodies" experiment re-created at Pisa, 2009 Oct12 | 4:02: Jump to 2:30.
6. Note momentum and angular momentum are useful quantities, which we will explicate a bit below. But you do understand momentum in concrete sense. A dust grain hitting you at 10 m/s is very different from a car hitting you at 10 m/s. The first you don't feel, the second you avoid at all costs.
7. momentum and angular momentum.
   1. torque
   2. spin (intrinsic angular momentum)
10. How is mass different from weight.
    1. F = mg = w = weight, but if g is constant as approximately near the Earth's surface, then m and w and proportional.
    2. Is mass quantity of matter. Yes and no. Better to say rest mass is quantity of matter, but that gets us off into special relativity which the story for another day.
13. Why are astronauts weightless in space.
    1. free fall
    2. Actually, free-fall frames are the true inertial frames to which all physical laws are referenced (aside from quibbling), except general relativity which tells us what inertial frames are. But there are lots of approximate inertial frames like any point on the surface of the Earth.
    3. File: Orbit file: newton_cannonball.html.
14. If you take off in a rocket accelerating upward:
    1. Actually, they mean perception of weight: i.e., weight plus g-force.
    2. A little math starting from Newton's 2nd law of motion (AKA F=ma) applied to the vertical direction with up positive on you and every atom of you:

         ma = F_net = F_pressure - mg 
         m(Δa + a_rocket) = F_pressure - mg 
         mΔa = F_pressure - mg - ma_rocket
         mΔa = F_pressure - m(g+a_rocket) 
         If you are at rest in the rocket,
         0 = F_pressure - m(g+a_rocket) 
         F_pressure = m(g+a_rocket) 

       Every layer of your body must exert a pressure force to make that layer and every layer above move with the rocket. You feel compressed. Here the g-force is ma_rocket. Note gravity and the g-force act on you atom by atom. Pressure forces are contact forces. Something has to touch for them to be exerted.
    3. But what if a_rocket = -g, then

         F_pressure = m(g+a_rocket) = 0  

       and feel weightless. There are NO pressure forces on you or in you. You and everything in the rocket are just floating around. You are in free fall. Of course, if you try to accelerate relative to the rocket, you need forces which will often be pressure forces of some kind or another.
17. Newton's laws of motion.
    1. Nix.
18. How did Isaac Newton (1643--1727) change our view of the universe?
    1. Nix.
20. Newton's 2nd law of motion (AKA F=ma)
    1. It is useful because we have force law (fundamental and emergent) that allow us to predict accelerations and changes in momentum.
28. conservation of momentum
    1. If F_net=0 in Newton's 2nd law of motion (AKA F=ma), then a = 0 and momentummv is constant.
    2. Newton's cradle
29. conservation of angular momentum holds when the net torque.
    1. central force CANNOT exert a torque about themselves.
31. conservation of angular momentum:
    1. File: Sport file: sport_videos.html.
32. Where do objects get their energy?
    1. conservation of energy principle.
39. E=mc**2
    1. File: Relativity file: e_mc2.html.
40. conservation of energy principle
    1. cosmological redshift
    2. dark energy
    3. general-relativity energy-momentum conservation equation (see also Car-120).
46. Newton's law of universal gravitation.
    1. Nix.
49. Objects orbit their common center of mass.
    1. File: Mechanics file: center_of_mass_fosbury_flop.html.
    2. barycenter
    3. File: Orbit file: orbit_elliptical_equal_mass.html.
    4. File: Orbit file: orbit_circular_large_mass_difference.html.