Physics notes (Giancoli) PDF

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chapter 1 - basics 1.1 The Nature of Observation: necessary in science, designing and performing exps Science e.g. Aristotle  and Galileo’s  perceptions of an object moving across  horiz surface 1.2 Physics and Other Fields

Aristotle: “bc objects always end up stopping, the natural state is rest!”

1.3 Models, Theories, Laws

Galileo, the first true experimentalist: “if friction can be removed, an object could move forever . . . motion is just as natural as rest. . . y’all look” -- a conceptual jump

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Theories: explain/order observations, accepted based on exp’s results, NOT dir fr observations

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Testing ideas/theories

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Theories NEVER “proved” bc can’t test for every possibility

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New theories usually accepted if they can explain a wider range of things than the old one

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E.g. Copernicus upped Ptolemy bc his theory explained Venus’s moonlike phases too

 1.4 Measurement, Uncertainty, Sig Figs   

Also judged based on how well they can qualitatively predict phenomena Until 2-ish centuries ago science was seen as 1 whole nat. philosophy Physics used in many fields -- zoology, physical therapy, elec. equip., architecture  Scientists use models  to understand certain phenomena -- analogy Allows for deeper understanding Makes way for new exps. or ideas of other related things  Model vs. theory: models are simple, structurally similar to phenomenon; theory broader, can give quant. testable predictions  Law: concise yet general encapsulations of how nature works Principle: less general than a law

Uncertainty: uncertainty in any measurement Limited accuracy in measuring devices: on a metric ruler w/ mm as smallest divisions, measurements are only precise to 1mm bc hard to interpolate  btwn divisions Estimated uncertainty should be included in any measurement (e.g.8.8±0.1 cm) Percent uncertainty: percent ratio of uncertainty to measured Loading… Uncertainty not usually specified outright, so assume it’s w/in 1-few units of the last specified digit  Significant figures: # of reliably known digits in # When doing calculations w/ measurements, can’t assume there are 10000 sig figs, because uncertainty is there MULTIPLYING/DIVIDING: # sig figs = that of number w/ smallest # sig figs ADDING/SUBTRACTING: # sig figs = that of number with most uncertainty (23 more uncertain -- to the units -- than 23.45 -- to the hundredths)  Scientific notation lets you clearly see sig figs TO FIND SIGS IN SCI NOTATION: put everything in the same order of magnitude of the largest # (e.g. if you have 8.2x10^3 and 0.0008x10^-6, put them all to 10^3) and THEN use sig figs fr there  Precision: repeatability -- how many times are you getting the same result? Accuracy: how close are you to the “true” value? 

1 kg = 2.2 lbs 1 in = 2.54 cm 1 amu = 1.6605 x 10–27 kg

chapter 2 - kinematics 2.1 Reference Frames

mechanics: study of motion, force, E 2 parts: kinematics (how objects move) and dynamics (force/WHY objects move)

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THIS CHAPTER: translational motion: motion w/o rotating use particle model of particle as a point w/o size -- useful when we’re only interested in translational motion

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any measurement made w/ respect to reference  frame -- must always specify in instances it can be confused

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use coordinate axes to describe the direction of motion

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for 1-D motion, use x axis alone to describe position -- unless vertical motion

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DISTANCE VS DISPLACEMENT: displacement: how far object is fr origin

2.2 Average Velocity

∆x = x2 - x1

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describe with vectors (related to velocity bc vectors)

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distance traveled is sum of the whole route

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average speed: distance traveled/total time

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avg of all instantaneous speeds technically so if a track has a dip in it smth will finish rolling along it faster than without the dip (though both will end w the same speeds) bc more instantaneous speed during dip

2.3 Instantaneous Velocity 

average velocity ( ): displacement/time

Loading…

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Always state that time  interval is the time during pd of observation

2.4 Acceleration   

instantaneous velocity: avg. velocity over INFINITESIMALLY small time interval

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Loading…

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● whenever txtbk says “velocity” it means instantaneous, not avg

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**** instantaneous speed always = magnitude of instantaneous velocity

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WHAT WHY?? bc dist travelled and magnitude of displacement become the same if you crunch them small enough

  2.5 Motion at Constant Acceleration

 acceleration: changing velocity average acceleration ā: ā =Loading… instantaneous acceleration a: Loading…

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deceleration: slowing down BUT doesn’t necessarily mean accl is negative -- if smth moving to left on axis and starts moving to right, that’s deceleration too

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best indicator: when velocity and accl point in opp dirs

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**** the kinematic equations for constant acceleration:

velocity, position, velocity squared, avg. velocity

2.7 Freely Falling Objects    

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1. that’s reasonable 2. position = orig pos + distance + avg velocity (a is the change in v so you find the average velocity from there -- causing the 1/2 -- and then mult. w/ another t) 3. vel squared = orig vel squared 4. average v. . . like c’mon you can remember that #  4 IS ONLY IF a IS CONSTANT!!!   5. level horizontal range (can also derive this)

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  speed of falling objects not proportional  to mass all objects at a given location on earth fall w/ same constant a if there is no air/air resistance

acceleration due to gravity: g = 9.80 m/s2 = 32 ft/s2 vector headed downwards to center of earth w/ objects in freefall, use the times-square equation, only with y instead of x (bc vertical motion) v = 0 at thrown object’s highest pt

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chapter 3 3.1 Vectors and vectors: have a direction and magnitude Scalars e.g. velocity , displacement , force, momentum  represent with arrows  symbol for vectors are always in bold w tiny arrows:   scalars: just a magnitude   3.2 Addition of vectors along the same axis can be added/subtracted regularly Vectors (Graphically) BUT if y and x, must find total displacement vector with them triangles  

this is called the resultant displacement

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can only use pyth thm when vectors are perp!!

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the vector equation for this is

Vector equation

VECTORS add up, but MAGNITUDES don’t unless the vectors point in the same dir

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-- bc that’s how triangles work: hyp MUST be less than sides!

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NOTE: the notation w the arrow (vector notation) must be set equal to a magnitude AND a direction (e.g. 11 km 25 degrees E); if w/o arrow you’re only talking abt the magnitude scalar (11 km)

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2 RAD WAYS TO ADD VECTORS:

Vector addition   

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(the llgm method is easier for you to conceptualize: if i pull one way and he pulls another, the box moves along the middle!)

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 3.3 Subtraction of Vectors + of a vector has the while magnitude of every vector positive, a negative  Multiplication opp DIRECTION with a Scalar vectors can also be multiplied by a scalar of c  BUT: while magnitude changes by factor of c, direction is the SAME     horiz component: Vcosx (hypotenuse times cosine)  vert component: Vsinx  FOR INCLINED PLANES IT’S THE OPP: mgsintheta for horiz, mgcostheta  for vert Projectile Motion use to resolve vectors into components so you can add/subtract even if not perp  projectile motion: translational motion of objects moving 2d through air near surface of Earth usually can ignore air resistance consider motion AFTER being projected into air, so only accl to consider is g BUT if projected vertically DO consider vy0

object dropped vertically hits ground @ same time as object thrown horiz, bc travels same vertical motion

chapter 4 - dynamics (newton’s laws) 4.1 Force

dynamics: link btwn force and motion force: push/pull, vector

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contact forces vs force  of gravity

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to change velocity/accl need force

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force can be measured w s  pring scale

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4.2 Newton’s 1st Law

as friction down, force needed to move down so in IDEAL frictionless world, moving object would keep going in straight line

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to push an object at rest, F must balance the force of friction @ that moment

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net force (sum of all vector force) accelerating

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is zero if not

NEWTON’S 1st LAW: object continues in state of rest or uniform velocity in straight line, so long as there is NO net force

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inertia: tendency to maintain state of uniform velocity

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INERTIAL REF FRAMES:

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1st law not applicable in all ref frames: e.g if a car stops and you move forward, it’s because of inertia, which is NOT actually a force

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BUT phys is easier within inertial ref frames (usually fixed on Earth or with constant velocity) where 1st law does apply

 4.3 Mass

 mass: measure of object’s inertia (up mass is up force needed to change accl, aka up inertia) SI unit: kg mass is an object’s intrinsic property, weight is a force (pull of grav) and depends object’s inertia same on the moon, but it WEIGHS less

4.4 Newton’s 2nd net force causes accl -- directly proportional but also dep on mass Law 

NEWTON’S 2nd LAW:

, again only valid in inertial ref frams

thus f orce can be defined as action capable of accling object

SI units: force is newton  (N) = 1 kg m / s2, mass is kg 

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in cgs, force is dyne  = 1 g cm / s2, mass is g  

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in imperial, force is pound  (lb), mass is slug 

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NEWTON’S 3rd LAW: every action has an equal and opposite reaction (but the

4.5 Newton’s 3rd two opposing forces act on DIFF objects so they don’t cancel!!) Law 

every material can exert a force bc every material is somewhat elastic  (a lil)

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4.6 Weight and  caused by gravitational  force the Normal Force accl g

bc based on mass, smaller-mass Moon makes things weigh less

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, aka weight 

normal force FN: contact force acting PERP. to surface (“normal” means perp) 

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weight and normal force are equal and in opp dirs (which is why objects are stationary) B  UT not bc of 3rd law bc they act on the SAME object

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4.7 Solving Problems with Newton’s Laws 

bc net force is a vector sum, resultant can be found w pyth thm  free-body or force diagram: diagram showing forces acting ON an object, don’t need to draw forces it exerts on OTHERS bc don’t need that to solve

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if multiple objects, draw 1 for each

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in translational motion, forces can be drawn acting fr object’s center (not true for rotation or statics)

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tension T: force exerted on cord pulling object assuming cord has neglig. mass, T is same all along cord bc F=ma=0 if m=0 -- net force 0 means all forces on cord must add up

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T-mg=ma (upward pull minus gravity equals how much force is actually going up)

4.8 Friction 

kinetic friction: sliding friction Ffr acts in direction opposite to sliding About p  roportional to normal force when you stick in c  oeff of kinetic friction t hat’s found exper.  static friction: ll to surfaces even when not moving (e.g. when trying to push an object static friction is working against you until it starts to move, at which pt kinetic takes over) the pt where it starts moving is when you’ve exceeded the maximum force of static friction. so static friction is (with a c  oeff of static friction): 

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chapter 5 - circular motion 5.1 Kinematics of object moving in circ @ constant speed v is exping uniform circular Uniform Circular motion Motion magnitude constant, but DIRECTION continually changing, so still  continually accling  

accl:

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 the distance covered is the distance along the ARC

 if tends to 0, then obv the dist and angle covered are also v small, so the 2 vectors are almost parallel bc barely any change

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the change vector-- acceleration -- is thus basically perp. to the two almost-same vectors

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bc it points to center, it’s c  entripetal/radial

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acceleration

= Loading…

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object moving in circle @ const speed accl to center

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accl and v always perp bc v is tangent to pt on circle

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 oft. described in terms of frequency f and period T  (WHAT THE HELL) v=2pi r /T

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5.2 Dynamics of  Uniform Circular acc to 2nd law F=ma, any accling object must have net force acting on it, so Motion a net force is necessary for centripetal accling/for object to move in circle  magnitude of force

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bc accl points to center, force must also point to center of circle, sometimes called centripetal  force

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BUT “centripetal force” only descs direction of the NET force needed, doesn’t describe an entirely new separate force

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e.g. swinging a ball on a string? “centripetal force” is the tension n the string

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ALSO: there is no such thing as an outward “centrifugal force”: an outward pull is not what keeps a thing moving in circle, an inward pull  is

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outward force you feel is the equal and opposite one to the force you’re exerting inwardly

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proof: when stopping circl motion, ball doesn’t swoop straight out, perp. to the tangent, as it would if there was outward force -- instead swoops out in a tangent

 5.3 Highway Banked and Unbanked Curves           

can be found by subbing in aR for a in F=ma

 when moving along curve in car, can feel a “centrifugal force” pulling you to car’s side, but NO it’s actually bc you tend to move straight, but car curved, so to force you to follow the curve, friction fr seat or direct force fr car door forces you centripetal force on car supplied by friction btwn tired and road  when wheels roll normally, static friction  is exerted against them WHY? bc each part of the wheel rests against road indiv every second if static friction is less than mv2/r (centripetal force) then car will start to skid into straight path, at which pt the smaller kinetic friction takes over banking curves reduces skid chances: normal force exerted by banked road will have a component pting to circle center, decreases reliance on friction alone as the force

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for a given banking angle, there will be a certain speed where NO friction is required: when horiz component (one pting to center) of

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normal is equal to the centripetal force

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this will hold for a certain design speed

5.4 Nonuniform Circular Motion

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 circ motion happens if net force goes to center of circle, but WHAT IF it’s at an angle?? component F  R directed to center factors into centripetal accl and keeps circular motion component F  tan which is tang. to circle increases/decreases speed, causes atan (just  basic change in v / change in t) thus when speed in circl motion changes, a tangential force component is being exerted bc the two accls are always perp, the total vector accl can be found with pyth thm!! bless pythagoras's ghost

5.5 Newton’s Law so, like, what EXERTS the force of gravity? it’s a force that acts even w/o contact of Universal centripetal accl of Moon div by accl of g  on Earth is 1/3600, and the Moon Gravitation 

is 60x further away fr center of the Earth than things on Earth’s surface are (HMMMM A LOT OF 60 AND 3600)

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ended up w law  of universal gravitation: every particle in universe attracts every

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other particle w a force that is given by the inverse  square law 

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looks a helluva lot like Coulomb’s law G is a universal constant measured exp. capital G:

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should be pretty small bc we don’t notice attraction btwn everyday-sized objects

 and G  w above eq bc: 5.6 Gravity Near can relate g the Earth’s Surface

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that final eq can by applied to other planets too!!

5.7 Satellites and SATELLITE MOTION: “Weightlessness”

satellites go into orbit by being accled to high enough tangential speed

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usually put into circular orbits bc reqs less speed

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they “stay up” bc of their high speed: if stopped moving, would fall, but bc of speed, constantly trying to fling out into tangent path but pulled in by Earth’s gravity so technically. . . it’s constantly falling around Earth satellites in circles need centripetal  accl vsq/r and the force is g  

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so combine F=ma w the eq relating g  to G  to get

ALSO: if you solve for v, m cancels out -- satellite’s speed doesn’t dep on its own mass

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WEIGHTLESSNESS:

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things can experience a  pparent weightlessness

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ex: a bag hanging in an elevator exps upward force w bc hanging, downward force mg bc that’s the bag’s weight

      5.8 Kepler’s Laws KEPLER’S LAWS

bc no accl, F=ma=0, so w-mg=0 -- the forces cancel!! BUT what if accl? then w-mg=ma, so w= ma+mg if accl is negative enough to...