Welcome to Phys 144! Newtonian mechanics and Relativity

Welcome to Phys 144!Newtonian mechanics andRelativity Dr. Jeff Gu, a humbled geophysicist

Me… Me… Me…--------------An ordinary talent who happens to be doing what he likes to do (or “doing the only thing he is somewhat capable of doing”---My Significant Other). About Me: 1. NO CRIMINAL RECORD, one $200 Speeding Ticket (paid in full)--- otherwise safe driver, like watching/listening all sports, plays a little bit of the flute, decent at table tennis and basketball, reading everything non-scientific (shamefully, that includes Harry Potter series). Background: 1. Born and raised in China, went to High School in the US 2. BSc. in Physics, MSc. in geophysics and computer science, PhD in Physics What got me out What got me in

Logistics ---- see Course Description, furthermore,

Main Course Goals • Physics Background Calibration • Solid understanding of Newtonian mechanics • Problem solving/insight enhancement • Beyond formula memorization • Emphasize insights and Evaluation • Introduce Calculus • Introduce Einstein's Special Relativity • First step beyond classical (Newtonian) physics • Will challenge your concepts of space and time!

Why Study Physics? To understand the properties of the universe we live in, i.e., to apprehend space-time, forces, matter, energy, power, interaction of matters The ‘feel-good’ Reasons: The thrill of being on the brink of discovery is second only to being madly in love. All science is either physics or stamp collecting.Ernest Rutherford When you are courting a nice girl an hour seems like a second. When you sit on a red-hot cinder a second seems like an hour. That's relativity. Albert Einstein ‘Practical’ benefits: Can try to use Heisenberg uncertainty principle to talk your way out of a traffic ticket. ON ‘Practical’ benefits: “Physics is like sex: sure, it may give some practical results, but that’s not why we do it.” ----- Richard Feyman

What is Physics? What is Physics? It is many things, depends...

A more practical reason, to get your precious degree In Physics (curriculum) 144 Newtonian Mechanics 146 281 Fluids and waves Electricity and Magnetism 244 Classical Mechanics 381/481 Electromagnetism 211 Thermodynamics 271 “Modern” physics 351 362 Special Relativity Optics 311/411 Statistical Mechanics 372 Quantum Mechanics Ma Ph 468 General Relativity 415 Condensed matter physics 472 Advanced Quantum mechanics 484 Nuclear physics 485 Particle physics 234 (a little bit of every thing+ geophys) Computational Physics (Yours Truly’s favorite)

In physics, your solution should convince a reasonable person. In math, you have to convince a person who's trying to make trouble. Ultimately, in physics, you're hoping to convince Nature. And I've found Nature to be pretty reasonable.   Frank Wilczek (Nobel price laureate) Regarding Calculus: Let go of the fear… "Do not worry too much about your difficulties in mathematics, I can assure you that mine are still greater." • Albert Einstein (second by Yours Truly) God does not care about our mathematical difficulties. He integrates empirically. Albert Einstein However, Yours Truly does: Check following link (for a simple integral/derivative calculator) http://www.1728.com/calcprim.htm

Problem Solving Suggestions Disclaimer: These are general strategies, may not be appropriate in all cases! ●Write down what you know and what the question asks you to calculate ■ Helps you identify any missing pieces of information you need which is the first step to finding them! ●Draw a diagram if appropriate ■ Can be essential in solving some types of problem ■ Allows you to assemble the information from the question as you read it ■ Be careful: an inaccurate diagram may make the question seem impossible or lead to a wrong result …

●Solve things symbolically (i.e, numbers at the end)! ■ Quicker: ‘g' times ‘m' is easier than 9.8 times 73.2 kg ■ Mistakes less likely ■ One solution: if a parameter changes, e.g. 'g' on Moon vs. Earth, it is easy to plug in the new value ■ Easy to check Units: Replace symbols by their units and ensure the result agrees with what you expect ■ Easy to understand Special Cases: e.g. what happens when 'g' goes to zero? ●Check units and/or dimensions ■ If you are calculating a length and get units of kilograms something is wrong! ●Check via common sense ■ My nephew said on his quiz paper that a trout for dinner (bought by mom) has the mass of 2 grams, well, there isn’t much to eat! Do an order of magnitude calculation. Out-of-worldly answers are found here

Units S.I. system allows for prefixes to the unit name to denote multiples of the unit:

Units • Originally base units derived from objects: • Platinum-iridium bar defined the metre • Platinum-iridium cylinder defined the kilogram • Second defined in terms of earth's rotation • Derived types: Force = ma = kg m/s2 = N (Newton) • Increasing understanding of physics allowed these to be defined more accurately... • Second defined as time needed for 9,192,631,770 oscillations of the electro-magnetic wave emitted from an atom of caesium-133 • One metre is the distance travelled by light in 1/299,792,458 seconds • Defined this way because we now know the speed of light to be a universal constant (see relativity later)

Mass • ...unfortunately, mass is still defined by the platinum-iridium block! • Why? - we do not really understand mass • No fundamental understanding about what causes it • No universally constant mass which can accurately scale up to everyday sizes e.g. electron=9.1x10-31kg! • Future particle physics • may provide a more physical measure.

A little bit of a trivia on dimensionality length scale mass scale time scale

Unit Conversion • Since multiple units exist for the same quantity it is often useful to convert between them • After a party, your friend is driving his Honda Civic at approx. 40 ms-1 on Whitemud, what is the next thing that will happen? • Answer: a date with the Police • SI is what we usually used in this course, but in real life, conversions may be necessary 1 in = 2.54 cm = 0.0254 m 1 ft = 30.48 cm = 0.3048 m 1 yard = 91.44 cm = 0.9144 m 1 mile = 1.6093 Km = 1609.3 m oC = (oF - 32) / 1.8 K = oC + 273.15 1 OZ = 28.35 g 1 lb = 0.4536 kg = 453.6 g

Why we to be careful with Units • Confusion can arise 1 us gal = 3.7854 litres (check that gas price!!) 1 imp gal = 4.546 litres Sometimes it is more serious than confusion on the gas prices: • NASA lost its Mars Orbiter spacecraft due to a failure to convert from the US version of imperial to metric units

Dimensional Analysis • Dimensional analysis is a good way to check the consistency of mathematical relations • A 'dimension' refers to the physical nature of a property • mass [M], length [L], time [T] etc. (= base units!) • For all physical equations the dimensions on both sides must match • Note that the reverse is NOT true: not all equations that have matching dimensions have physical meaning! • e.g. F=ma and F=½ma both pass dimensional analysis since the ½ is dimensionless but only F=ma has physical meaning with S.I. units

Order of Magnitude Calculations and Units “Powers of 10” As an example, my students and I put in seismometers in the field. The station stays out there for months and need to write to a flashcard (4 GB). How long can the flashcard last out there with a sample rate of 20 samples/sec for 3 channels? Well, here is what I do for a conservative Estimate (don’t do this in exams, only as a way to quickly get an approximate answer): Each channel: 20 samples/sec x 4 bytes/sample = 80 bytes/sec ~ 100 bytes/sec 3 channels ~ 300 bytes/sec 1 day: 300 bytes/sec x 4000 sec/hour x 24 hours/day (say 25, easier) = 3.0 x 107 bytes/day ~ 30 MB/day How many days: 4048 MB (say 4000) / (30 MB bytes/day) ~ 130 days ~ 4-5 months

Other ‘Review’ Concepts from Chapter 1 Have fun reviewing some of the topics in Chapter 1 (some will be explained next time). Reminder: The SI System of Units – the main focus in my exams mass (kg), length (m) and time (s) Significant Figures My policy on sig. figs. during exams: no calculator dumps I leave the explicit instruction on exams to assume that all numbers given are taken to be exact, so two or three sig figs should suffice. However your labs, which explicitly involve measured values and error, will have a different policy, and much of your effort in your labs and lab prep will be devoted to estimating errors and their propagation, and sig figure issues become critical. Your lab T.A. will explain how this works. Next Trigonometry and Vectors (a review)

Experimental Uncertainties You'll cover this in more detail in the labs! Very important concept: without it you cannot believe any result that you hear! For example, if someone claims that the chance of Obama getting re-elected is 55.28% according to a recent poll of 2000 people and Sarah Paulin is ~45.72%, are you happy with the statement? In short, without errors and more premises these numbers are meaningless!! • Obvious loop holes: who are those surveyed, what demographic, and what’s up with the decimal places (i.e., are these surveys that good or simply computer dumps)? • Even take these for face value, need to know errors since there is a big difference between:and:

Scalars – physical quantities that can be specified uniquely by a magnitude (and an associated unit where appropriate). Scalars encountered in Phys 144: distance, time, speed, mass, work, energy, power, moment of inertia * Also we will often consider any pure number like 0, 1, 2, π, e ≈ 2.71828… to be scalars. * The result of any single experimental measurement is a real-valued scalar. Vectors– physical quantities that require both a magnitude and a direction to specify them (and an associated unit where appropriate) Vectors to encounter in Phys 144: displacement, velocity, acceleration, force, momentum, torque, angular momentum In N-dimensions, N numbers are required to specify a vector.

Sometimes care needs to be taken: • Speed is a scalar • e.g. "He was travelling at 108km/h on the Whitemud when he had the accident" • Velocity is a vector: something travelling at a constant speed can have a non-constant velocity • e.g. the moon orbits the earth at (approximately) a constant speed. However the moon's velocity is constantly changing as it is always accelerating towards the earth. • Speed is the magnitude of the velocity When Michael Phelps or Usain Bolt get to the finish line, SUPPOSE I am in the same races/meet (I know… chances=0), do I have higher or lower VELOCITY than they do at that instance? What about the average speed?

Coordinate Systems and Vector Representations Thus in two dimensions we need two numbers to specify a direction. The simplest description is with an ordered pair of numbers each of which describes ‘how much’ the vector points along a given perpendicular axis. This leads to the component representation of a vector. These all represent the same vector. They all have the same magnitude and direction. Displacement Vector ■ Notations 2D 3D Common Notations (personally, I go with bold or top arrow)

** Vectors can be split into component vectors (decomposition into orthogonal vectors) ** Vectors can be split into component scalars multiplied by the corresponding unit vectors ** magnitude of a given vector (scalar, looks like absolute value, ‘length’) 2D ** Vectors can be split into component scalars multiplied by the corresponding unit vectors ** Similarly, for 3D,

Magnitudes and Standard Unit Vectors DEFINE: in 2D in 3D (by vector addition and scalar multiplication) Vector Representations using standard unit vectors: An adventurer is surveying a cave. She follows a passage 180 m straight west, then 210 m in a direction 45° east of south, then 280 m at 30° east of north. After a fourth unmeasured displacement she finds herself back where she started. Use the method of components to determine the magnitude and direction of the fourth displacement.

Vector Addition (in this particular system) Given vectors and i.e. to add vectors you add their components. What about subtraction (A-B) ?? Treat it as adding a negative B to A.

Example of vector addition At a road bend: A car travels at N30˚E for 5 km and changes bearing to N60˚E, compute the total displacement vector and its orientation. N 0° 6km 5km W 270° E 90° S 180° Solution: add these vectors first decompose each into its north and east components (x and y axes)

Trigonometry • Need to know well: sine, cosine, tangent • The three functions are defined as: Hypotenuse Opposite Adjacent • Also the inverse functions: Warning: Careful with your calculators, say for inverse tan, it always goes from 0-90 deg. For those of you who program, also need to think of radians.

Vector Addition We can now add each of the components of the same direction together since they are parallel vectors: • Now use the previous example of combining two perpendicular vectors to get the final distance and direction from the starting point

Vector Addition (in this particular system) Given vectors and i.e. to add vectors you add their components. What about subtraction (A-B) ?? Treat it as adding a negative B to A. Scalar Multiplication Given a vector and a scalar , scalar multiplication is DEFINED as Example That is When we write we really mean: Multiplication (a) Dot Product (or ‘scalar product’)

In component/matrix form: Special case: one of the vectors is a unit vector (magnitude=1), dot product gives the component of the ‘other’ vector in the direction of the unit vector, (b) vector Product (or ‘cross-product’, a vector) The resultant vector from a cross product is perpendicular to both vectors (following a right-handed rule), The direction… The magnitude…

Cross product in component form, To compute the determinant Note: the alternating sign for the middle element!

Some simple properties: and (product of magnitudes) If are parallel and If are perpendicular Other properties of the dot product: (commutative and distributive) Where will we see it? Work: Basic Calculus Differentiation: if y=f(x) then the first derivative of y is simply the slope (gradient) at each position. (1) polynomials:

(2) Product rule: Deductive thinking: how can I find derivative of g/h? (3) Chain rule: i.e., (4) Trigonometric functions: (5) log/exponential functions:

Integration: the area between a and b along x-axis and a line defined by a function f(x) is given by the integral of f(x) between a and b. (1) polynomials: (2) Polynomials with limits: Can do similar operations for trig and log functions. Basic rule of thumb: Differentiation and integration are opposite operations. Verify your integration result by differentiating it. Don’t forget the constant for ‘Open’ integrals (no limits).

Welcome to Phys 144! Newtonian mechanics and Relativity