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

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

Intensity intensity = power delivered per unit area in watts/m 2 point source intensity is inverse-square with distance

Universal Law of Gravity all matter is weakly attracted the force is an inverse-square law where G = 6.67x N·m 2 /kg 2 Example: Two 100kg persons stand 1.0m apart

Gravity causes differential (rather than constant) pull on large objects. This causes: orbital lock of moon with earth ocean tides on earth

Spring Tides (largest)

Neap Tides (smallest)

Solar Eclipse Solar Eclipse, moon blocks light heading toward earth (shown above) Lunar Eclipse, earth blocks light from sun heading toward moon Eclipses

Einstein modeled gravity as stretched space-time

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 period 2 ~ average radius 3

Projectile Motion is motion when only gravity acts Horizontal force is zero  Horizontal velocity constant. Vertical force is weight  Vertical velocity is decreasing.

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

Distance of Fall d = ½ gt 2 with g = 10m/s/s t = 1sd = 5m t = 2sd = 20m t = 3s d = 45m Example: h = 15m, projectile fired horizontally at 6 m/s. Calculate the Range.

Another way to see “distance of fall” in projectile motion

11 Atomic Physics protons, neutrons, electrons and atoms atomic number and isotopes nucleus size and Rutherford’s Experiment elements, molecules, compounds, and mixtures

Atomic History Hypothesized in 5 th Century B.C. (Greece) Aristotle 4 th 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

Atomic Imagery resolving power = size of smallest feature we can see electron microscopy ~ um visible light microscopy ~ 0.2um size of atom ~ um

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 Rutherford’s Experiment

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

The Periodic Table of The Elements (the distinct atoms)

Molecules Molecules are groups of atoms. Here are a few examples. oxygenammonia methane water

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.solidatoms moleculesions

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.

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 energyannihilateenergy

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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