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Physics For Teachers (PS.122 - §203, 2018 Spring => CRN 4619)
Class Meets in :    Science 179 ... Tue & thRs   3:00pm - 4:50pm
My office:   Science 159 (below ramp to 3rd Ave)     e-mail :   foltzc @ marshall.edu     phone :   (304) 696-2519

Topic 1 (Items & Properties − Static Measurement with Units)

Quiz 1 was Jan.30 ... here's my grading key as jpeg image .


A. Properties: Measurement Procedure & Units

measure means compare some property to a standard
objects have various properties ... length, mass, color, hardness, speed, weight, usefulness, cost, value, beauty, etc.

any well-defined property must have some procedure to rank objects by.
      example: hardness is ranked by a scratch test : the one that gets scratched is "less hard".
      some poorly-defined properties depend on the observer (which, in the list above? 2 lines before )

some properties depend on the environment that the object is in (which, in the list above? 3 lines before )
      weight is heaviness, which occurs because Earth's gravity pulls the mass of that object downward
      . . . the same object weighs much less on the Moon, and 4% less at Earth's North Pole than at its equator.

properties that do not depend on the environment are said to be intrinsic to the object
      mass describes how much material the object has ... so is intrinsic to the object
      . . . and does not change unless you remove some of the object's material (the remaining piece is a distinct object than it had been)
      . . . the total mass contained in both pieces (the sum, when their values are added together) is the same as the original mass.

some properties change as time goes by, or vary as something else about that object changes
      a large portion of science is to figure out what causes these properties to change,
      ... and how (=> why) one variable property relates to the other (one goal: which causes which?)
      any base property must be constant, or at least we must be able to synchronize with its passage.

some constant properties can be compared quantitatively with the same property of another object.
      comparing means that you count how many of the smaller are equivalent to the larger
      . . . examples : length, mass, cost . . . 200 fast-food burgers cost about the same as a cheap laptop
. . . properties that are additive are quantities - numbers are quantities, because they add.
      Physical Science is almost exclusively concerned with quantities
      . . . otherwise the count would be pretty useless
      notice: if 400 burgers cost the same as 2 laptops, then their cost is a quantity
. . . counter-example 1: in gymnastics, two "5.1" scores is not equivalent to a "10.2" score
. . . counter-example 2: a "6" on Moh's hardness scale is not twice as hard as a "3"


1. Length or distance

it is useful (to communicate effectively) to compare with some standard object .
      The standard object is made (chosen) so that it has Unit value ("1") in this property.
. . . if this property is length, the standard object's length will be exactly 1 inch , or exactly 1 foot , or exactly 1 meter ... by definition.
      You report a measured value for some object's property as a count of the Unit ... "of" means multiplied by !
      ( the number of unit properties that make up the other object's property )
. . . I am as tall as 5½ 1-foot rulers ... much taller than 5½ 1-inch spacers ... not nearly as tall as 5½ 1-meter sticks
=> always append the appropriate UNITS after every number ... the number is almost meaningless without them!

whenever you add or subtract two (measured) values , to get a new (derived) quantity ,
      they MUST have the same Units !
. . . to figure out the height of my head , when I'm standing on an 18" chair, you need to add my height to the chair's height.
      head Habove floor = head Habove chair + chair Habove floor   <=   there is a pattern among the modifiers !
            = 5½ ft + 18 in = 5½ ft + 18 in × (1 ft / 12 in) = 5½ ft + 1½ ft   <=   how to "convert" Units : multiply by ("1") !
      . . . = (5½ + 1½) ft = 7 ft   <=   both numbers are multiplied by ft , so collect that factor before adding .
. . . see if you can use inches to do that addition . . .

2.a. mass ... the "amount of matter" in an object , is a conserved scalar

the total mass seems to always be the same.
. . . if the mass inside a container decreases, then some mass left the container and is now outside it.
      if the mass inside is increasing, it must be getting in (through the surface) somehow.
. . . scientific explanation is based on conserved quantities, like mass.
      (taking $100 from your bank account thru an ATM, does not change the total amount you have)
. . . "adding         property from all objects" is something we'll do often
      we abbreviate "Sum them all" by   "Σ" ;   it is the Greek "S" (named "Sigma") , means to sum them all
=> Σ mbefore = Σ mafter   . . . read it as "the Sum of  masses  is constant"

mass carries the property of inertia
. . . the tendancy to stay put , or to keep moving in a straight line at constant speed
. . . measured in   kilograms   in our (mks) metric system
      a 1-ton compact car has 1000 kg , my body mass is about 65 kg , a gallon of milk holds about 4 kg .
. . . a 2000 kg big 4x4 pickup truck is twice as hard (2×) to get going, or stop from moving, as a 1000 kg compact car.
=> mass tends to not change its motion

2.b. weight ... gravity's pull to an object

mass , in a gravity field , is pulled downward (causing weight).
. . . mass is a scalar - one value , no directionality implied
      it describes the matter inside the object , as opposed to outside it
. . . weight is a vector - a downward pull . . . a kind of Force   (any push or pull is a Force)
      caused by Earth's gravity , it differs slightly from place to place
      because gravity is more intense some places than others
. . . Force is usually reported in   Newtons   , abbreviated   N   , which really is a   kg·m/s /s
      because Newton (the person, long ago) said that Force causes mass (kg) having velocity (m/s) to change over time (/s) .

gravity itself is a property of the environment. . . gravity is the propensity to pull ... it permeates every thing , and extends thru all space ... a field
      g intensity is a bit less than 10 Newton/kg on Earth's surface (9.76 - 9.87)
. . . Earth's gravity pulls every bit of matter downward (toward its center)
      the property of matter that is influenced by gravity is mass
=> Fgravity = m g . . . = "weight" . . . abbreviating gravity's intensity as   g .

3. time ... a parameter that continues to change for all physical things

we invented calendars and clocks to keep track of time
. . . but we can't even control how fast we go thru time - (or how slow time goes by us)
      we certainly can't choose "when to be", in that parameter ...
. . . all unit systems measure time in   seconds  
      60s = 1 minute; 3600s = 1 hour; 86.400ks = 1 day; 604.8ks = 1 week ; 2600ks ≈ a month ; 31.5Ms ≈ 1 year

4. electric charge or current ... charge is conserved (like mass is), and also has a tendancy to keep its motion

more on charge and electric current in the second half of the course

B. Base Units and converting Units

we abbreviate names for common properties
      for example, length (L), width (W), height (H), mass (m), time (t)
Other properties depend on these, so are called derived properties.
      Area (A,) is L × W ... (or L × H , or W × H) . . . Volume (V) is A × H .

whenever you multiply or divide two (measured) values , to get a new (derived) quantity ,
      always do the same computation with the units ... they're multiplied by those numbers !
. . . to figure out the Area of a desktop , that has L = 4 ft , W = 30 in ,
      A = L × W = 4·ft × 30·in = 4 × 30 · ft×in = 120 · ft×in .
      . . . that set of units looks peculiar , but it is correct . . . but could be avoided :
      A = L × W = 4·ft × 30·(1/12 ft) = 4 × 2½ · ft×ft = 10 · ft² . . . <= convert by substitution (1 in = 1/12 ft)

In modern times, everybody measures width and length in the same base unit that height is measured in
      (they extend in different directions, but the same procedure can be used to measure)
. . . in the prior example we knew that 4 ft really meant 48 inches ... foot is not independent from inch, 1 ft = 12 in.
      to be consistent (in our present technology) we only have a few (5 or 6) to be used as base units.
The US has allowed the metric system to be used since 1790, and has required the metric system to be accepted (for any transaction) since 1866;
      we've required that any label be defined from metric units since 1893, and finally began to require metric units in 1985.
. . . but we still sometimes see units from the SAE or FPS or US Customary unit set ;
      they are based on inch or foot, second, pound, Coulomb, candle, °Farenheit   (base units)
. . . System International (SI) "metric" base Units are :   meter , kilogram, second, Ampere, candle, Kelvin ... so SI is sometimes called mks.
distances and locations are measured in meters
masses are measured in kilograms
time intervals (durations) are measured in seconds.

We will usually allow the Force unit   Newton   , abbreviated   N   , to replace   kg m/s²
      (because we get tired of writing that mess of symbols) - but it is not really

We usually try to avoid using large numbers
. . . 6 friends can talk in a dorm room; 50 people fill our classroom; what do 30,000 look like? 30,000,000?
      we can use different units to describe different "size scales" ... inches, feet, furlongs, miles
      ok - how many inches in a foot?       how many feet in a furlong?       in a mile?
      . . . how many miles in a   um ,   hmm   - whatever is next ?
      ok - how many ounces in a pound?       pounds in a ton?       um, tons in a ___
      ok - how many fluid ounces in a pint?       pints in a gallon?       gallons in a ... bushel? barrel?       bushels in a ___
. . . is there a pattern among these numbers?       what pattern is starting to show?

SI has International words for large numbers of units:
. . . kilo   means thousand
. . . Mega   means million
. . . Giga   means billion (American = British thousand million)
. . . Tera   means trillion (US = British billion = million million)
SI has International words for fractional units:
. . . milli   means thousandth
. . . micro   means millionth
. . . nano   means billionth (US)
. . . pico   means trillionth (US)
I hope everybody recognizes the pattern among these numbers ... (and that pattern continues on ...)

Astronomy often uses Earth's value for some property as the standard unit,
. . . so that some other planet is being compared to Earth
or they use the Sun's value, so other stars will be compared to the Sun.
Earth's distance from the Sun is called an "astronomical unit"
. . . that would be 108 solar diameters, or 216 solar radii.
Our Moon's mass is 1/81 of Earth's mass, but its radius is 27% of Earth's
. . . so what is its volume? (.27×.27×.27 = 0.020 = 1/50 of Earth's)


C. Directional quantities are called vectors

Where something is ... its Place or Location or Position ; abbreviated "x" .
North is not East, North is not up . . . and East is opposite West ...
. . . Charleston is about 50 miles from Huntington , East from here
      not at all the same place as Martin county KY (50 mi South)!
. . . Huntington is mile 8 , Charleston is mile 52 (the "0" is at the KY/WV border, so exit numbers are Eastward)

Displacement = change in place , in some direction
Δx = place change = "after place" − "before place" = xafter − xbefore
. . . as you travel from Huntington to Charleston , your (East-West) displacement is :
      Δx = 52 mi (E) − 8 mi (E) = 44 mi (E) .
. . . as you travel from Charleston to Milton , your displacement is   Δx = 28 mi (E) − 52 mi (E) = −24 mi (E) . . . = 24 mi Westward .
      as you travel from Huntington to Milton , your displacement is 20 mi Eastward .
      . . . no matter what route you use (even Hunt → Charls → Milton)

travel distance is Length along your own path
      a path does not need to be in an objectively constant direction (like "East") so direction is irrelevant.
. . . you always travel along your path , never against your path
      so travel distance can never be negative , never cancels previous distance
. . . Hunt → Milt is 20 mi , if travel is directly there
      but Hunt → Charls → Milt would be   44 mi + 24 mi = (44 + 24) mi = 68 mi .

D. products ... one property multiplied by another property

some products are themselves meaningful quantities:

1. Surface Area
. . . top surface : A = W×L
      points upward, out from the object underneath
. . . front surface : A = W×H
      points backward, out from the object in front of it
. . . right surface : A = L×H
      points rightward, out from the object to its left.

2. Volume contained inside
. . . V = W×L·H , scalar quantity (not directional)
      but does distinguish interior from exterior.

3. mass moment :   the "first moment" of mass is   m x
. . . determines where the effective center is , for an extended body
      that is where it balances ... where you push to move it most effectively
      a free object will spin (rotate) around that place, without wobbling.
. . . if it is symmetric , its average location is its center ... the average of its two edges (in each direction)
      a basketball spins around its center (on a finger) ... so does a frisbee (even in flight)
. . . if it is not symmetric , the physically important place is its mass center , or center-of-mass
      that is the average place for each of its parts ... "weighted" by their mass
. . . multiply each mass by where it is, then add all those mx terms to get the total MX.
      always   multiply   before   adding . . .
. . . m1x1 + m2x2 + m3x3 + ... = MtotalXtotal
      this product "mass moment" is a meaningful quantity of its own because it does add up to a useful total
=> Σ ( m x )   = Mtotal Xc.o.m.   . . . divide total mass moment by total mass M , to locate the center-of-mass

There are situations that have a different aspect (rather than mass) being most important
. . . the nearest edge (for avoiding a collision) , or the bottom edge (for rolling on)
use the "first moment" procedure to determine the "center-of-_____" place   for any other aspect
. . . the center of Area ... center of population ... center of business ... center of age ...
      all that is needed is for that aspect to be described by numbers

4. Rotational inertia , the second moment of mass ... m x²
. . . compute mass · (d ² ) for all of its parts
      called the second moment of intertia because location is taken to the second power
. . . the distance d is usually measured from a rotation axis
      measure from center-of-mass, if there is no externally-attached axis
=> it is harder to start something spinning, if its mass is far from the axis
      (and spinning skaters spin faster as they pull their arms in, closer to the axis)


E. Ratios and Proportions . . . "per portion" . . . implies division !

1. Density is any property per Volume . . . divided by Volume
. . . a "cholesterol number" tells how concentrated the cholesterol is, in blood ... mine is 134 grams per 100 liter
. . . population density for land animals is usually reported per Area instead of per volume
mass density is mass divided by Volume
      mass density describes how "compact" a material is ... it's the same for any size object
      . . . since you've divided the big object into several "unit Volumes" (pretending to separate one of them)
      water's mass density is 1 kg / liter = 1 kg / (.1m × .1m × .1m) = 1000 kg / m³   <= check that with your own calculator!
. . . mass density is the first material ratio that people recognized
      we abbreviate it with   ρ   lower case Greek "r" , named "rho" , for being an important ratio ... it is not a latin "p"
=> ρ = m / V   . . .
. . . densities usually describe how things are found (not explain why they are that way)

2. any property divided by mass is called "specific"
. . . specific Volume is the object's Volume divided by its mass
      it describes how sparse (spread-out "fluffy") the material is
      notice that it is the reciprocal of mass density . . . (ρ is preferred)
. . . specific nutrition is the nutritional content in one mass unit of some food type
      a big jar (0.794 kg) of peanut butter has 373 grams fat, 175 grams protein, 72 grams sugar
      ... so eack kilogram of that peanut butter has 470 grams fat, 220 gram protein, 90 gram sugar
      ... any amount of peanut butter is   47% fat, 22% protein, 9% sugar (by mass or weight)
=> a "specific" quantity becomes a property of the material , not the object

densities and specific quantities are intensive , not extensive
. . . this means that they don't depend on how big (extension) the object is
      only on how concentrated that quantity is, in the material

3. Angles
. . . A. one angle measurement compares an arc length to the full circle circumference.
. . . Example; my hand spans about 8" along the arc of a basketball
      basketballs are 29½" all the waqy around (circumference)
=> my hand spans  8"/29.5"   = 0.27 . . . about ¼ of the circle

B. another angle measurement compares an arc length to the radius
. . . the basketball is round, so its circumference should be ... 2 π R
      so R = 29.5" / (2 π) = 4.7"   (Radius)
=> my hand covers  8"/4.7"   = 1.7 radians . . . angle around the center.
      (called a radian , having been compared to the radius)

If you measure my hand as 200 mm and the ball as 749 mm circumference
. . . my hand covers the same fraction of the ball (27% around) and the same angle (1.7 rad)
=> fractions and percentages and radians are unitless measures.

A larger hand would stretch across a larger angle.

A smaller ball would be more fully covered by the same size hand;
. . . a softball is easy to "palm"
a ball twice as large would have only half the angle covered
. . . nobody can palm a medicine ball.
 
3. angles in degrees

We often follow ancient Babylonian tradition and measure angles using degrees .
. . . there are 360° in an entire circle, so a right angle, ¼ circle, includes 90°.
. . . there are 2 π R radians in an entire circle, so there are π/2 rad = 1.5708 rad in ¼ circle.

The skinny wedge on left of the middle line is 1° wide (there's one on the right of the middle line also)
. . . it is 1 length unit wide (at the widest), 57 length units distant from the center ... (= 90° / 1.571 rad/deg)
. . . the larger wedge on the right is 10 units wide, so is about 10° ... 10/57 rad ≈ 1/6 rad

Babylonians split each degree into 60 "minute" portions ... 60 arc-minutes per degree.
. . . So, the arc-minute is one length unit wide, but 60 x 57 units distant . . . (~3500)
      the face diameter of the Moon (or Sun) is about ½° wide, so each is about 30 arc-minutes wide.
      ... abbreviated 30' ...

Modern Astronomers continued that tradition by splitting each arc-minute a second time, into 60 arc-seconds!
. . . so, an arc-second is one length unit wide, but 60 x 60 x 57 units distant (~200,000)
that is, 1" wide at a distance of about 200,000 inches ( ~ 20,000 feet ~ nearly 4 miles!)
. . . you need binoculars or small telescope to discern an arc-second!


3.b. Large angles
used in backyard viewing can be estimated by "rules of thumb"
. . . for example, my thumb-tip to pinky-tip is about 20 cm wide (spread)
      when my arm is straight, my hand is 57 cm from my eye.
=> my hand spans about 20° when my arm is straight.

People with bigger hands usually have longer arms, too ... so the ratio (angle) is about the same.
. . . My thumb is about 6 cm long, so looks 6° long, my pinky-nail 1° wide.
as a comparison, Sun and Moon are each about ½° (32 arc-minutes) diameter
. . . typical human eye can see thousands of detail features on Moon's surface
      able to resolve marks that are a dozen arc-seconds apart.

These large angles are usually for measuring angular separations
. . . how far is the Sun above the horizon
      (which tells me how much time before sunset/dusk)
. . . how far the Moon is from the Sun
      (=> how bright the Moon will be and when it will set)


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