“If we worked on the assumption that what is accepted as true really is true, then there would be little hope for advance” - Orville Wright “No flying machine will ever fly from New York to Paris... [because] no known motor can run at the requisite speed for four days without stopping.” - Orville Wright

Skills - Gravitation Correctly apply universal law of gravitation: Spherical symmetry / small objects, c.m. (<< r) / No force inside spherical shell Find satellite speeds for circular orbits Use conserv of L to find satellite speed in elliptical orbit, given speed elsewhere in same orbit. (Kepler #2) Understand difference between weight and apparent weight (astronauts in orbit are falling!) Understand implications of elliptical orbits (e.g., you can’t throw a rock into orbit! Why not?) Find escape speed from a spherical planet.

Skills - Periodic Motion Memorize relationships between T, f,  Predict changes in motion when mass is added to or removed from a mass-spring system, at different points in its oscillation Given sufficient information (spring constant, mass, initial conditions) predict where a mass will be at a later time. (This means writing down the equation of motion correctly!) (Find k! Either from a known force and displacement, F- -kx, or from the frequency and mass in SHM) Given equation  sqrt(k/m), solve angular SHM problems by analogy! Apply simple pendulum equation (to be given). Apply physical pendulum equation (to be given). YOU MUST memorize what d and I mean in this equation.

Skills - Fluids Understand density and pressure. Pressure is same at same depth in same (stationary) fluid. Use to calculate mechanical advantage in a hydraulic lift. Understand difference between gauge pressure and total pressure. Apply P=  gh (given) correctly. When can it NOT be used? Solve buoyancy problems, even if two fluids are involved (Use FBDs when needed!) Apply Bernoulli to solve for flow velocity, or for pressure, or height, for incompressible flows. (BE will be given).

Skills - Waves Given wavelength and frequency, write down the mathematical description of a wave moving in either the + or - direction. Apply (given) equation for speed of waves on a string. Memorize and appy relationship between frequency, wavelength, and wave speed. Understand difference between transverse and longitudinal waves. Memorize that power & intensity are proportional to amplitude squared. Apply inverse square law for waves in 3D. Use principle of superposition to sketch interfering waves (on a string). Understand what a standing wave is, and predict frequencies for overtones on a violin string.

An incompressible fluid flows through a constriction, as shown. The speed of the fluid is A] faster at (a) than at (b) B] faster at (b) than at (a) C] the same speed at both places

The fluid moves faster at (b) because A] being incompressible, the smaller cross-sectional area forces the velocity to be higher B] there is a pressure drop from (a) to (b) that accelerates the fluid C] either is a legitimate viewpoint, but I prefer B, as it helps me to understand Bernoulli.

In which tube would the fluid rise higher? Or choose [C], the fluid would rise to the same height in both tubes? The pressure at b is lower, so the fluid will not rise as high in tube b. Note: Pascal’s principle (equal pressures at equal heights) applies to static fluid only! There is a subtlety here: we do NOT apply Bernoulli to points A and B directly, because they are not “connected” by smooth (laminar) flow lines.

Curve balls, topspin etc. Not Bernoulli, but Magnus!

Waves

Sinusoidal Waves