8 Rotation

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8 Rotation

• tangential speed changes with radius from axis
• mass distribution (and amount) determines
  rotational inertia
• torque force x lever-arm
• angular momentum rotational inertia x
  rotational speed
• conservation of angular momentum can be used to
  interpret rotational collisions and interactions

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9 Gravity

• Newton's law of gravity universality, mass
  dependence, distance dependence
• light propagation and the inverse square law
• origin and effect of tidal forces

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Intensity

• intensity power delivered per unit area in
  watts/m2
• point source intensity is inverse-square with
  distance

4
Universal Law of Gravity

• all matter is weakly attracted
• the force is an inverse-square law
• where G 6.67x10-11 Nm2/kg2
• Example Two 100kg persons stand 1.0m apart

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Gravity causes differential (rather than
constant) pull on large objects. This
causes orbital lock of moon with earth ocean
tides on earth
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Spring Tides (largest)
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Neap Tides (smallest)
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Eclipses
Solar Eclipse
Solar Eclipse, moon blocks light heading toward
earth (shown above)
Lunar Eclipse, earth blocks light from sun
heading toward moon
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Einstein modeled gravity as stretched space-time
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10 Projectile Motion

• Projectile motion is a combination of horizontal
  motion at constant velocity and vertical free
  fall
• satellite motion is projectile motion
• gravity does work on objects in elliptical orbits
• kinematic equations used to calculate range or
  distance of fall for horizontally released
  projectiles
• Kepler's laws
• elliptical orbits
• equal areas in equal times
• period2 average radius3

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Projectile Motion is motion when only gravity acts
Horizontal force is zero ? Horizontal velocity
constant. Vertical force is weight ? Vertical
velocity is decreasing.
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Each component affects range
vertical component affects time of flight Range
(horizontal component) x (time of flight) as
angle increases (time of flight) increases as
angle increases (horizontal component) decreases
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Distance of Fall

• d ½ gt2 with g 10m/s/s
• t 1s d 5m
• t 2s d 20m
• t 3s d 45m

Example h 15m, projectile fired horizontally
at 6 m/s. Calculate the Range.
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Another way to see distance of fall in
projectile motion
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11 Atomic Physics

• protons, neutrons, electrons and atoms
• atomic number and isotopes
• nucleus size and Rutherfords Experiment
• elements, molecules, compounds, and mixtures

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Atomic History

• Hypothesized in 5th Century B.C. (Greece)
• Aristotle 4th Century B.C. did not believe in
  atoms. Taught 4-element idea (earth, air, water,
  fire)
• Dalton 1800s England revived atomic idea
• Brown 1827 hypothesized atoms caused oscillation
  of microscopic particles
• Today we know 88 naturally occurring atoms and
  about 30 more lab created

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Atomic Imagery

• resolving power size of smallest feature we can
  see
• electron microscopy 0.0005 um
• visible light microscopy 0.2um
• size of atom 0.0002 um

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What do Atoms Look Like?

• middle of the atom is nucleus which is composed
  of protons and neutrons
• outside of atom is an electron shell
• atom is mostly empty space
• this was confirmed by Rutherfords Experiment

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Elements and the Atomic Number

• Atomic Number is the number of protons in a
  nucleus,
• this number determines which element the atom is.
• Isotopes are atoms with the same number of
  protons but different number of neutrons

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The Periodic Table of The Elements (the distinct
atoms)
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Molecules
Molecules are groups of atoms. Here are a few
examples.
oxygen ammonia methane water
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A crystal is a solid in which the constituent
atoms, molecules, or ions are packed in a
regularly ordered, repeating pattern extending in
all three spatial dimensions.
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Terminology

• Element group of atoms with the same number of
  protons.
• Compound chemical substance formed from 2 or
  more elements and which has a definite chemical
  formula. Compounds do not have to be formed from
  molecules since compounds can be crystal
  structures such as table salt.
• Mixture substance with components that have not
  combined chemically.
• Chemical Substance - an element, compound, or
  mixture.
• Molecule smallest particle of chemical
  substance that has the same composition and
  chemical properties, e.g. water molecule.

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Anti-matter anti-proton same mass as proton
but oppositely charged anti-electron (positron)
same mass as electron but with opposite charge. a
particle and its antiparticle annihilate each
other in a burst of energy
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Dark Matter
Universe appears to be about 4 visible and 96
dark. There are various theories about what
makes up this mass.
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End