1
If we worked on the assumption that what is
accepted as true really is true, then there would
be little hope for advance - Orville
WrightNo 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
2
Skills - Gravitation

• Correctly apply universal law of gravitation
• Spherical symmetry /
• small objects, c.m. (ltlt 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 cant throw a rock into orbit! Why
  not?)
• Find escape speed from a spherical planet.

3
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.

4
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).

5
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.
6
An incompressible fluid flows through a
constriction, as shown. The speed of the fluid
isA faster at (a) than at (b)B faster at
(b) than at (a)C the same speed at both places
7
The fluid moves faster at (b) becauseA being
incompressible, the smaller cross-sectional area
forces the velocity to be higherB there is a
pressure drop from (a) to (b) that accelerates
the fluidC either is a legitimate viewpoint,
but I prefer B, as it helps me to understand
Bernoulli.
8
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.

• 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 Pascals principle
(equal pressures at equal heights) applies to
static fluid only!
9
Curve balls, topspin etc. Not Bernoulli, but
Magnus!
10
Waves
11
Sinusoidal Waves