425 Head First Physics Free download ebook

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Adva nc e Pra ise for

H e a d First Physic s

“If you want to learn some physics, but you think it’s too difficult, buy this book! It will probably help,

and if it doesn’t, you can always use it as a doorstop or hamster bedding or something. I wish I had a copy of this book when I was teaching physics.”

— John Allister, physics teacher

“Head First Physics has achieved the impossible - a serious textbook that makes physics fun. Students all over will be thinking like a physicist!”

— Georgia Gale Grant, freelance science writer, communicator and broadcaster

“Great graphics, clear explanations and some crazy real world problems to solve! This text is full of strategies and tips to attack problems. It encourages a team approach that’s so essential in today’s work world.”

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“This is an outstandingly good teacher masquerading as a physics book! You never feel phased if you don’t quite understand something the first time because you know it will be explained again in a different way and then repeated and reinforced. ”

— Marion Lang, teacher

“This book takes you by the hand and guides you through the world of physics.”

— Catriona Lang, teacher

“Head First Physics really rocks - I never thought it was possible to enjoy learning physics so much! This book is about understanding and not about rote learning, so you can get to grips with the physics and remember it much better as a result.”

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Pra ise for ot he r

H e a d First

a c a de m ic t it le s

“Head First Statistics is by far the most entertaining, attention-catching study guide on the market. By presenting the material in an engaging manner, it provides students with a comfortable way to learn an otherwise cumbersome subject. The explanation of the topics is presented in a manner comprehensible to students of all levels.”

— Ariana Anderson, Teaching Fellow/PhD candidate in Statistics, UCLA

“Head First is an intuitive way to understand statistics using simple, real-life examples that make learning fun and natural.”

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“Thought Head First was just for computer nerds? Try the brain-friendly way with statistics and you’ll change your mind. It really works.”

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“Down with dull statistics books! Even my cat liked this one.”

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Pra ise for t he

H e a d First

Approa ch

“There are books you buy, books you keep, books you keep on your desk, and thanks to O’Reilly and the Head First crew, there is the ultimate category, Head First books. They’re the ones that are dog-eared, mangled, and carried everywhere. Head First SQL is at the top of my stack. Heck, even the PDF I have for review is tattered and torn.”

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“I feel like a thousand pounds of books have just been lifted off of my head.”

—Ward Cunningham, inventor of the Wiki and founder of the Hillside Group

“This book’s admirable clarity, humor and substantial doses of clever make it the sort of book that helps even non-programmers think well about problem-solving.”

— Cory Doctorow, co-editor of Boing Boing Author, Down and Out in the Magic Kingdom

and Someone Comes to Town, Someone Leaves Town

“It’s fast, irreverent, fun, and engaging. Be careful—you might actually learn something!”

—Ken Arnold, former Senior Engineer at Sun Microsystems

Co-author (with James Gosling, creator of Java), The Java Programming Language

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Ot he r re lat e d book s from O’Re illy

Statistics HacksTM Statistics in a Nutshell Mind HacksTM

Mind Performance HacksTM Your Brain: The Missing Manual

Ot he r book s in O’Re illy’s H e a d First se rie s

Head First JavaTM

Head First Object-Oriented Analysis and Design (OOA&D) Head First HTML with CSS and XHTML

Head First Design Patterns Head First Servlets and JSP Head First EJB

Head First PMP Head First SQL

Head First Software Development Head First JavaScript

Head First Ajax Head First Statistics

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Beijing • Cambridge • Kln • Sebastopol • Taipei • Tokyo

Heather Lang, Ph.D.

Head First Physics

A learner’s companion to

mechanics and practical physics

Wouldn’t it be dreamy if there was a physics book that

was more fun than going to the dentist, and more revealing than an IRS form? It’s probably just a

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H e a d First Physic s by Heather Lang, Ph.D.

Published by O’Reilly Media, Inc., 1005 Gravenstein Highway North, Sebastopol, CA 95472.

O’Reilly Media books may be purchased for educational, business, or sales promotional use. Online editions are also available for most titles (safari.oreilly.com). For more information, contact our corporate/institutional sales department: (800) 998-9938 or corporate@oreilly.com.

Se rie s Cre at ors: Kathy Sierra, Bert Bates

Se rie s Edit or : Brett D. McLaughlin

De sign Edit or : Louise Barr

Cove r De signe rs: Louise Barr, Steve Fehler

Produc t ion Edit or : Brittany Smith

I ndexe r : Julie Hawks

Print ing H ist or y:

September 2008: First Edition.

The O’Reilly logo is a registered trademark of O’Reilly Media, Inc. The Head First series designations,

Head First Physics, and related trade dress are trademarks of O’Reilly Media, Inc.

Many of the designations used by manufacturers and sellers to distinguish their products are claimed as trademarks. Where those designations appear in this book, and O’Reilly Media, Inc., was aware of a trademark claim, the designations have been printed in caps or initial caps.

While every precaution has been taken in the preparation of this book, the publisher and the authors assume no responsibility for errors or omissions, or for damages resulting from the use of the information contained herein. No pizza delivery guys were harmed in the making of this book.

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viii

the author

Author of Head First Physics

Heather studied physics in Manchester, gaining a first class honours degree. She likes explaining how stuff works and persuading people to send her chocolate in the post. Her first foray into science communication was via the BaBar Particle Physics Teaching Package. She followed this up with a Ph.D. in the grey area between physics and biochemistry, but got fed up of sharing a fridge with petri dishes and moved on from the lab into education and Head First Physics.

When not explaining how stuff works, Heather likes to play extreme sports such as chess and cricket, play with sliders on a sound desk, or play the fool while running school chess clubs (in the name of teaching of course).

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table of contents

ix

Table of Contents (Summary)

Table of Contents (the real thing)

Your brain on Physics.

Here you are trying to learn something, while here your brain is doing you a favor by making sure the learning doesn’t stick. Your brain’s thinking, “Better leave room for more important things, like which wild animals to avoid and whether naked snowboarding is a bad idea.” So how do you trick your brain into thinking that your life depends on knowing physics?

I nt ro

Who is this book for? xxxiv

We know what you’re thinking xxxv

Metacognition xxxvii

Bend your brain into submission xxxix

Read me xl

The technical review team xlii

Acknowledgments xliii

Intro xxxiii

1 Think Like a Physicist: In the beginning ... 1 2 Making It All Mean Something: Units and Measurements 17 3 Scientific Notation, Area, and Volume: All Numbers Great and Small 55 4 Equations and Graphs: Learning the Lingo 95

5 Dealing with Directions: Vectors 149

Experiments 193

6 Displacement, Velocity, and Acceleration: What’s Going On? 203 7 Equations of Motion (Part 1): Playing with Equations 237 8 Equations of Motion (Part 2): Up, Up, and... Back Down 283 9 Triangles, Trig and Trajectories: Going Two-Dimensional 335 10 Momentum Conservation: What Newton Did 391 11 Weight and The Normal Force: Forces for Courses 437 12 Using Forces, Momentum, Friction and Impulse: Getting On With It 471

13 Torque and Work: Getting a Lift 515

14 Energy Conservation: Making Your Life Easier 559 15 Tension, Pulleys and Problem Solving: Changing Direction 603 16 Circular Motion (Part 1) From α to ω 631 17 Circular Motion (Part 2): Staying on Track 663 18 Gravitation and Orbits: Getting Away From It All 715 19 Oscillations (Part 1): Round and Round 761 20 Oscillations (Part 2): Springs ‘n’ Swings 797 21 Think Like a Physicist: It’s the Final Chapter 839 i Appendix i: Top Six Things We Didn’t Cover 863

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x

Physics is the world around you 2

You can get a feel for what’s happening by being a part of it 4 Use your intuition to look for ‘special points’ 6 The center of the earth is a special point 8 Ask yourself “What am I ALREADY doing as

I reach the special point?” 9

Where you’re at - and what happens next? 11

Now put it all together 13

I n t he be ginning ...

think like a physicist

1

Physics is about the world around you

and how everything in it works. As you go about your daily life, you’re doing physics all the time! But the thought of actually learning physics may sometimes feel like falling into a bottomless pit with no escape! Don’t worry... this chapter introduces how

to think like a physicist. You’ll learn to step into problems and to use your

intuition to spot patterns and ‘special points’ that make things much easier.

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2

It’s the best music player ever, and you’re part of the team! 18 So you get on with measuring the myPod case 19 When the myPod case comes back from the factory, it’s way too big 20 There aren’t any UNITS on the blueprint 22 You’ll use SI units in this book (and in your class) 25 You use conversion factors to change units 29 You can write a conversion factor as a fraction 30 Now you can use the conversion factor to update the blueprint 33 What to do with numbers that have waaaay too many

digits to be usable 36

How many digits of your measurements look significant? 37 Generally, you should round your answers to three significant digits 39 You ALREADY intuitively rounded your original

myPod measurements! 42

Any measurement you make has an error (or uncertainty)

associated with it 43

The error on your original measurements

should propagate through to your converted blueprint 44 STOP!! Before you hit send, do your answers SUCK?! 47 When you write down a measurement,

you need the right number of significant digits 51

Hero or Zero? 52

U nit s a nd m e a sure m e nt s

making it all MEAN something

How long is a piece of string?

Physics is based on making

measurements that tell you about size. In this chapter, you’ll learn how to use

units and rounding to avoid making mistakes - and also why errors are OK.

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3

A messy college dorm room 56

So how long before things go really bad? 57 Power notation helps you multiply by

the same number over and over 61

Your calculator displays big numbers using scientific notation 63 Scientific notation uses powers of 10 to write down long numbers 64 Scientific notation helps you with small numbers as well 68 You’ll often need to work with area or volume 72 Look up facts in a book (or table of information) 73 Prefixes help with numbers outside your comfort zone 74 Scientific notation helps you to do calculations with

large and small numbers 76

The guys have it all worked out 81

200,000,000 meters cubed bugs after only 16 hours is

totally the wrong size of answer! 83 Be careful converting units of area or volume 84 So the bugs won’t take over ... unless the guys sleep in! 86 The “Converting units of area or volume” Question 87

All num be rs gre at a nd sm a ll

scientific notation, area, and volume

The Bumper Book of Bugs

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4

You need to work out how to give the customer their delivery time 97 If you write the delivery time as an equation,

you can see what’s going on 98

Use variables to keep your equation general 99 You need to work out Alex’s cycling time 101 When you design an experiment, think about what might go wrong! 105 Conduct an experiment to find out Alex’s speed 108 Write down your results... in a table 109 Use the table of distances and times to work out Alex’s speed 111 Random errors mean that results will be spread out 113 A graph is the best way of taking an average of ALL your results 114 Use a graph to show Alex’s time for ANY distance 117 The line on the graph is your best estimate for

how long Alex takes to cycle ANY distance 118 You can see Alex’s speed from the steepness

of the distance-time graph 120

Alex’s speed is the slope of the distance-time graph 122 Now work out Alex’s average speed from your graph 123 You need an equation for Alex’s time to give to the web guys 125 Rearrange the equation to say " time = something" 126 Use your equation to work out the time it takes

Alex to reach each house 129

So just convert the units, and you’re all set...right? 131 Include the cooking time in your equation 133 A graph lets you see the difference the stop lights made 137 The stop lights change Alex’s average speed 139 The “Did you do what they asked you” Question 146

Le a r ning t he lingo

equations and graphs

Communication is vital.

You’re already off to a good start in your journey to truly think like a physicist, but now you need to

communicate your thoughts. In this chapter, you’re going to take your

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xiv

5

Ve c t ors

dealing with directions

The treasure hunt 150

Displacement is different from distance 155 Distance is a scalar; displacement is a vector 157 You can represent vectors using arrows 157

You can add vectors in any order 162

The “Wheat from the chaff ” Question 166

Angles measure rotations 168

If you can’t deal with something big, break it down

into smaller parts 170

Velocity is the ‘vector version’ of speed 174

Write units using shorthand 175

You need to allow for the stream’s velocity too! 176 If you can find the stream’s velocity, you can figure

out the velocity for the boat 177

It takes the boat time to accelerate from a standing start 180 How do you deal with acceleration? 181 Vector, Angle, Velocity, Acceleration = WINNER!!! 187 I’m ready - what’s first?

Time, speed, and distance are all well and good, but you really

need DIRECTION too if you want to get on in life.

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6

Just another day in the desert ... 204

How can you use what you know? 207

The cage accelerates as it falls 210

‘Vectorize’ your equation 211

You want an instantaneous velocity, not an average velocity 213 You already know how to calculate the slope of a straight line... 218 A point on a curved line has the same slope as its tangent 218 The slope of something’s velocity-time graph

lets you work out its acceleration 226 Work out the units of acceleration 227 Success! You worked out the velocity after 2.0 s -

and the cage won’t break! 231

Now onto solve for the displacement! 234

What ’s going on?

Displacement, Velocity, and Acceleration

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xvi

7

How high should the crane be? 238

Graphs and equations both represent the real world 240 You’re interested in the start and end points 241 You have an equation for the velocity -

but what about the displacement? 244

See the average velocity on your velocity-time graph 249 Test your equations by imagining them with different numbers 251 Calculate the cage’s displacement! 253 You know how high the crane should be! 254 But now the Dingo needs something more general 255

A substitution will help 256

Get rid of the variables you don’t want by making substitutions 259

Continue making substitutions ... 261

You derived a useful equation for the cage’s displacement! 264

Check your equation using Units 265

Check your equation by trying out some extreme values 268

Your equation checks out! 273

So the Dingo drops the cage ... 274

The “Substitution” Question 275

The “Units” or “Dimensional analysis” Question 276

Pla ying Wit h Equat ions

Equations of motion (part 1)

It’s time to take things to another level.

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xvii

8

Now ACME has an amazing new cage launcher 284 The acceleration due to gravity is constant 286 Velocity and acceleration are in opposite directions,

so they have opposite signs 288

You can use one graph to work out the shapes of the others 293 Is a graph of your equation the same shape

as the graph you sketched? 298

Fortunately, ACME has a rocket-powered hovercraft! 305 You can work out a new equation by making a substitution for t 308 Multiply out the parentheses in your equation 311 You have two sets of parentheses multiplied together 312 You need to simplify your equation by grouping the terms 315 You can use your new equation to work out the stopping distance 317 There are THREE key equations you can use

when there’s constant acceleration 318 You need to work out the launch velocity that gets

the Dingo out of the Grand Canyon! 321 You need to find another way of doing this problem 326 The start of a beautiful friendship 330 The “Sketch a graph” or “Match a graph” Question 331 The “Symmetry” and “Special points” Questions 332

U p, up, a nd... ba ck dow n

equations of motion (part 2)

- Launches a standard ACME cage straight up in the air.

- Variable launch speeds.

- Waterproof

- Payment plans and financing available

ACME

_{Cage Launcher}

1 2

- Top speed 43 m/s.

- Accelerates or brakes

at 2.5 m/s2_. - Financing Available.

ACME

_{Rocket-powered}

Hovercraft

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xviii

9

Camelot - we have a problem! 336

How wide should you make the moat? 339

Looks like a triangle, yeah? 340

A scale drawing can solve problems 342 Pythagoras’ Theorem lets you figure out the sides quickly 343 Sketch + shape + equation = Problem solved! 345 Camelot ... we have ANOTHER problem! 348 Relate your angle to an angle inside the triangle 351 Classify similar triangles by the ratios of their side lengths 354 Sine, cosine and tangent connect the sides and

angles of a right-angled triangle 355 How to remember which ratio is which? 357

Sine Exposed 358

Calculators have sin(θ), cos(θ) and tan(θ) tables built in 360

Uh oh. Gravity... 367

The cannonball’s velocity and acceleration

vectors point in different directions 369 Gravity accelerates everything downwards at 9.8 m/s2 ₃₇₀ The horizontal component of the velocity can’t change

once you’ve let go 371

The horizontal component of a projectile’s velocity is constant 372 The same method solves both problems 375

The “Projectile” Question 376

The “Missing steps” Question 387

Going t w o-dim e nsiona l

triangles, trig and trajectories

Ladder

Wall End of ladder

is nowhere near top of wall.

Bottom of ladder is at edge of moat.

Moat filled with water.

15.0 m

15.0 m _15.0 m

So you can deal with one dimension. But what about real life?

Real things don’t just go up or down - they go sideways too! But never fear - you’re about to gain a whole new bunch of trigonometry superpowers that’ll see you spotting

right-angled triangles wherever you go and using them to reduce complicated-looking

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10

The pirates be havin’ a spot o’ bother with a ghost ship ... 392 What does the maximum range depend on? 395 Firing at 45° maximizes your range 396 You can’t do everything that’s theoretically possible -

you need to be practical too 397

Sieges-R-Us has a new stone cannonball,

which they claim will increase the range! 400 Massive things are more difficult to start and stop 402

Newton’s First Law 403

Mass matters 404

A stone cannonball has a smaller mass -

so it has a larger velocity. But how much larger? 407

Here’s your lab equipment 410

How are force, mass and velocity related? 411 Vary only one thing at a time in your experiment 414 Mass × velocity - momentum - is conserved 418 A greater force acting over the same amount of time

gives a greater change in momentum 420 Write momentum conservation as an equation 421 Momentum conservation and Newton’s Third Law are equivalent 422 You’ve calculated the stone cannonball’s velocity,

but you want the new range! 429

Use proportion to work out the new range 430 The “Proportion” Question (often multiple choice) 434

What N e w t on Did

momentum conservation

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xx

11

WeightBotchers are at it again! 438

Is it really possible to lose weight instantly?! 439 Scales work by compressing or stretching a spring 440 Mass is a measurement of “stuff ” 442

Weight is a force 442

The relationship between force and mass involves momentum 444 If the object’s mass is constant, Fnet = ma 446 The scales measure the support force 449

Now you can debunk the machine! 451

The machine reduces the support force 452 Force pairs help you check your work 454

You debunked WeightBotchers! 456

A surface can only exert a force perpendicular (or normal) to it 458 When you slide downhill, there’s zero perpendicular acceleration 461 Use parallel and perpendicular force components to deal with a slope 463

The “Free body diagram” Question 466

The “Thing on a slope” Question 467

Forc e s for c ourse s

weight and the normal force

Lose weight

INSTANTLY!!

(for only $499)

Before

After!

Sometimes you have to make a statement forcefully.

In this chapter, you’ll work out Newton’s 2nd Law from what you already know about momentum conservation to wind up with the key equation, F_net = ma. Once you combine this with spotting Newton’s 3rd Law force pairs, and drawing free body

diagrams, you’ll be able to deal with (just about) anything. You’ll also learn about why

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xxi

12

It’s ... SimFootball! 472

Momentum is conserved in a collision 476 But the collision might be at an angle 477 A triangle with no right angles is awkward 479 Use component vectors to create some right-angled triangles 480 The programmer includes 2D momentum conservation ... 483 In real life, the force of friction is present 484 Friction depends on the types of surfaces that are interacting 488 Be careful when you calculate the normal force 489 You’re ready to use friction in the game! 491 Including friction stops the players from sliding forever! 492 The sliding players are fine - but the tire drag is causing problems 493 Using components for the tire drag works! 497

Friction Exposed 498

The “Friction” Question 499

How does kicking a football work? 500

F t is called impulse 502

The game’s great - but there’s just been a spec change! 506 For added realism, sometimes the players should slip 509 You can change only direction horizontally on a

flat surface because of friction 510

The game is brilliant, and going to X-Force rocks! 511 Newton’s Laws give you awesome powers 512

Ge t t ing on w it h it

using forces, momentum, friction and impulse

It’s no good memorizing lots of theory if you can’t apply it.

You already know about equations of motion, component vectors, momentum conservation, free body diagrams and Newton’s Laws. In this chapter, you’ll learn how to fit all of these things together and apply them to solve a much wider range

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xxii

13

Half the kingdom to anyone who can lift the sword in the stone ... 516 Can physics help you to lift a heavy object? 517 Use a lever to turn a small force into a larger force 519 Do an experiment to determine where to position the fulcrum 521 Zero net torque causes the lever to balance 525 Use torque to lift the sword and the stone! 530 The “Two equations, two unknowns” Question 533 So you lift the sword and stone with the lever ...

but they don’t go high enough! 535

You can’t get something for nothing 537 When you move an object against a force, you’re doing work 538 The work you need to do a job = force × displacement 538 Which method involves the least amount of work? 539

Work has units of Joules 541

Energy is the capacity that something has to do work 542 Lifting stones is like transferring energy from one store to another 542 Energy conservation helps you to solve problems

with differences in height 545

Will energy conservation save the day? 547 You need to do work against friction as well as against gravity 549 Doing work against friction increases internal energy 551

Heating increases internal energy 552

It’s impossible to be 100% efficient 553

Ge t t ing a lift

torque and work

You can use your physics knowledge to do superhuman feats.

In this chapter, you’ll learn how to harness torque to perform amazing displays of strength, by using a lever to exert a much larger force than you could on your own. However, you can’t get something for nothing - energy is always conserved and the amount of work

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xxiii

14

The ultimate bobsled experience 560

Forces and component vectors solve the first part...

but the second part doesn’t have a uniform slope 563 A moving object has kinetic energy 565 The kinetic energy is related to the velocity 567 Calculate the velocity using energy conservation

and the change in height 569

You’ve used energy conservation to solve the second part 571 In the third part, you have to apply a force to stop a moving object 571 Putting on the brake does work on the track 573 Doing work against friction increases the internal energy 574 Energy conservation helps you to do

complicated problems in a simpler way 579 There’s a practical difference between

momentum and kinetic energy 581

The “Show that” Question 584

The “Energy transfer” Question 585

Momentum conservation will solve an inelastic collision problem 587 You need a second equation for an elastic collision 587 Energy conservation gives you the second equation that you need! 589 Factoring involves putting in parentheses 591 You can deal with elastic collisions now 592 In an elastic collision, the relative velocity reverses 593 There’s a gravity-defying trick shot to sort out ... 594 The initial collision is inelastic - so mechanical energy isn’t conserved 596 Use momentum conservation for the inelastic part 597

The “Ballistic pendulum” Question 599

M a k ing your life e a sie r

energy conservation

Why do things the hard way when there’s an easier way?

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15

It’s a bird... it’s plane...no, it’s a guy on a skateboard?! 604 Always look for something familiar 605 Michael and the stack accelerate at the same rate 608

Use tension to tackle the problem 611

Look at the big picture as well as the parts 617 But the day before the competition ... 619 Using energy conservation is simpler than using forces 621

There goes that skateboard... 626

Cha nging dire c t ion

tension, pulleys and problem solving

The center of the target is 15.0 m from the foot of the pier. Skateboard is pulled along

the pier by the rope.

When the skateboard reaches the end of the pier, Michael continues with velocity v.

v

The mass has just hit the surface of the water.

11.0 m

15.0 m

With the correct initial velocity at the end of the pier, Michael will follow this trajectory and hit the bullseye. The competition takes

place when the tide is in and the sea is 110. m below the top of the pier.

H e re ’s w hat SH OU LD ha ppe n...

Sometimes you need to deal with the tension in a situation

So far, you’ve been using forces, free body diagrams and energy conservation to solve problems. In this chapter you’ll take that further as you deal with ropes,

pulleys, and yes, tension. Along the way, you’ll also practise looking for familiar

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16

Limber up for the Kentucky Hamster Derby 632 You can revolutionize the hamsters’ training 633 Thinking through different approaches helps 635 A circle’s radius and circumference are linked by π 637 Convert from linear distance to revolutions 639 Convert the linear speeds into Hertz 641 So you set up the machine ... but the wheel turns too slowly! 643 Try some numbers to work out how things relate to each other 645 The units on the motor are radians per second 646 Convert frequency to angular frequency 651

The hamster trainer is complete! 652

You can increase the (linear) speed by increasing the wheel’s radius 657

The “Angular quantities” Question 660

From α to ω

circular motion (part 1)

Hey kiddo, this Kentucky Hamster Derby is big business, and we gotta get

the training schedule absolutely spot on!

Billionaire hamster owner Distance

(km) Speed (km/h)

Total number of revolutions

Motor setting ( )

15.0 3.0 10.0 4.0 2.0 5.5

0 5 10 15 20 25

You say you want a revolution?

In this chapter, you’ll learn how to deal with circular motion with a crash course in circle anatomy, including what the radius and circumference have to do with pies (or should that be πs). After dealing with frequency and period, you’ll need to switch from the linear to the angular. But once you’ve learned to use

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17

Houston ... we have a problem 664

When you’re in freefall, objects appear to float beside you 666 What’s the astronaut missing, compared to when he’s on Earth? 667 Can you mimic the contact force you feel on Earth? 669 Accelerating the space station allows you

to experience a contact force 671

You can only go in a circle because of a centripetal force 674 Centripetal force acts towards the center of the circle 677 The astronaut experiences a contact force when you

rotate the space station 678

What affects the size of centripetal force? 679 Spot the equation for the centripetal acceleration 681 Give the astronauts a centripetal force 683 The floor space is the area of a cylinder’s curved surface 686

Let’s test the space station... 689

The “Centripetal force” Question 692

The bobsled needs to turn a corner 694 Angling the track gives the normal force a horizontal component 697 When you slide downhill, there’s no perpendicular acceleration 698 When you turn a corner, there’s no vertical acceleration 699 How to deal with an object on a slope 700 The “support force” required for a vertical circle varies 704 Any force that acts towards the center of the circle

can provide a centripetal force 707

The “Banked curve” Question 711

The “Vertical circle” Question 712

St a ying on t ra ck

circular motion (part 2)

The astronauts are tir

ed

of floating. They w

ant

gravity... in space!

Ever feel like someone’s gone off at a tangent?

That’s exactly what happens when you try to move an object along a circular path when there’s not enough

centripetal force to enable this to happen. In this chapter, you’ll learn exactly what

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18

Party planners, a big event, and lots of cheese 716 What length should the cocktail sticks be? 717

The cheese globe is a sphere 719

The surface area of the sphere is the same as

the surface area of the cheese 720

Let there be cheese... 723

The party’s on! 725

To infinity - and beyond! 726

Earth’s gravitational force on you becomes weaker

as you go further away 729

Gravitation is an inverse square law 735 Now you can calculate the force on the spaceship

at any distance from the Earth 741

The potential energy is the area under the force-displacement graph 743 If U = 0 at infinity, the equation works for any star or planet 745

Potential Energy Exposed 746

Use energy conservation to calculate the astronaut’s escape velocity 747 We need to keep up with our astronaut 751 The centripetal force is provided by gravity 754 With the comms satellites in place, it’s Pluto (and beyond) 757 The “gravitational force = centripetal force” Question 758

Ge t t ing a w a y from it a ll

gravitation and orbits

So far, you’ve been up close and personal with gravity

- but what happens to the attraction as your feet leave the ground? In this chapter, you’ll learn that gravitation is an inverse square law, and harness the power of gravitational potential

to take a trip to infinity... and beyond. Closer to home, you’ll learn how to deal with

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xxviii

19

Welcome to the fair! 762

Reproduce the duck on the display 763

The screen for the game is TWO-DIMENSIONAL 769 So we know what the duck does... but where exactly is the duck? 773 Any time you’re dealing with a component vector,

try to spot a right-angled triangle 774

Let’s show Jane the display 782

The second player sees the x-component of the duck’s displacement 783 We need a wider definition of cosine, too 784 sine and cosine are related to each other 785

Sine Exposed 787

Let the games begin! 788

What’s the duck’s velocity from each player’s point of view? 789 Get the shape of the velocity-time graph from

the slope of the displacement-time graph 790

The game is complete! 794

Round a nd round

Oscillations (part 1)

Things can look very different when you see them from

another angle.

So far you’ve been looking at circular motion from above - but what does it look like from the side? In this chapter, you’ll tie together your circular motion and

trigonometry superpowers as you learn extended definitions of sine and cosine. Once

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xxix

20

Get rocking, not talking 798

The plant rocker needs to work for three different masses of plant 798 A spring will produce regular oscillations 799

Displacement from equilibrium and

strength of spring affect the force 801 A mass on a spring moves like a side-on view of circular motion 805 A mass on a spring moves with simple harmonic motion 806 Simple harmonic motion is sinusoidal 809 Work out constants by comparing a situation-specific

equation with a standard equation 810

The “This equation is like that one” Question 813 Anne forgot to mention something ... 815

The plants rock - and you rule! 821

But now the plant rocker’s frequency has changed ... 822 The frequency of a horizontal spring depends on the mass 824 Will using a vertical spring make a difference? 824 A pendulum swings with simple harmonic motion 830 What does the frequency of a pendulum depend on? 831

The pendulum design works! 833

The “Vertical spring” Question 835

The “How does this depend on that” Question 836

Springs ‘n’ sw ings

Oscillations (part 2)

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xxx

21

You’ve come a long way! 840

Now you can finish off the globe 841

The round-trip looks like simple harmonic motion 842 But what time does the round-trip take? 843 You can treat the Earth like a sphere and a shell 845 The net force from the shell is zero 850 The force is proportional to the displacement, so your trip is SHM 853 The “Equation you’ve never seen before” Question 855 You know your average speed - but what’s your top speed? 857 Circular motion from side-on looks like simple harmonic motion 858

You can do (just about) anything! 861

I t ’s t he fina l cha pt e r

think like a physicist

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xxxi

i

#1 Equation of a straight line graph, y = mx + c 864 #2 Displacement is the area under the velocity-time graph 866

#3 Torque on a bridge 868

#4 Power 870

#5 Lots of practice questions 870

#6 Exam tips 871

T he Top Six T hings (w e didn’t c ove r)

leftovers

ii

Point of Re fe re nc e

equation table

No book can ever tell you everything about everything.

We’ve covered a lot of ground, and given you some great thinking skills and physics knowledge that will help you in the future, whether you’re taking an exam or are just curious about how the world works. We had to make some really tough choices about what to include and what to leave out. Here are some topics that we didn’t look at as we went along, but are still important and useful.

It’s difficult to remember something when you’ve only

seen it once.

Equations are a major way of describing what’s going on in physics. Every time

you use equations to help solve a problem, you naturally start to become familiar with them without the need to spend time doing rote memorization. But before you get to that stage, it’s good to have a place you can look up

the equation you want to use. That’s what this equation table appendix is for - it’s a point of reference that you can turn to at any time.

Learn

Practice Practice Practice Practice

Learn Learn Learn Learn

Start Finish

Better at physics

Trigonom e t r y

Pythagoras hyp2_{= opp}2_{+ adj}2

Sine sin(θ) = opp_hyp

Cosine cos(θ) = adj_hyp

Tangent tan(θ) = opp_adj hyp

ttt

adj

θ

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xxxiii

how to use this

book

I nt ro

In this section we answer the burning ques

tion:

“So why DID they put that in a physics book?”

I can’t believe they put

that

in a

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xxxiv intro how to use this book

Who is this book for?

Who should probably back away from this book?

If you can answer “yes” to all of these:

Don’t worry if you’re

missing the calculator -

they only cost a few dollars.

If you can answer “yes” to any of these: this book is for you.

this book is not for you.

[Note from marketing: this book is

for anyone with the cash to buy it.]

Do you have access to a pen and a scientific calculator? 1

1

Do you want to learn and understand physics by doing, rather than by reading, whether you need to pass an

exam at the end or not?

2 2

Do you prefer chatting with friends about interesting

things to dry, dull, academic lectures?

3 3

Are you someone who’s never studied basic algebra?

(You don’t need to be advanced, but you should be able to add, subtract, multiply and divide. We’ll cover everything else you need to know about math and physics.)

1 1

Are you a physics ninja looking for a reference book? 2

2

Are you afraid to try something different? Would you rather have a root canal than mix stripes with plaid? Do you believe that a physics book can’t be serious if it involves implementing a training schedule for thoroughbred hamster racing?

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you are here 4 xxxv

the intro

“How can this be a serious physics book?” “What’s with all the graphics?”

“Can I actually learn it this way?”

Your brain craves novelty. It’s always searching, scanning, waiting for something unusual. It was built that way, and it helps you stay alive.

So what does your brain do with all the routine, ordinary, normal things you encounter? Everything it can to stop them from interfering with the brain’s

real job—recording things that matter. It doesn’t bother saving the boring things; they never make it past the “this is obviously not important” filter.

How does your brain know what’s important? Suppose you’re out for a day hike and a tiger jumps in front of you, what happens inside your head and body?

Neurons fire. Emotions crank up. Chemicals surge. And that’s how your brain knows...

T his m ust be im por t a nt ! Don’t forge t it !

But imagine you’re at home, or in a library. It’s a safe, warm, tiger-free zone. You’re studying. Getting ready for an exam. Or trying to learn some tough

technical topic your boss thinks will take a week, ten days at the most.

Just one problem. Your brain’s trying to do you a big favor. It’s trying to make sure that this obviously non-important content doesn’t clutter up scarce resources. Resources that are better spent storing the really

big things. Like tigers. Like the danger of fire. Like how you should never have posted those photos on your Facebook page.

And there’s no simple way to tell your brain, “Hey brain, thank you very much, but no matter how dull this book is, and how little I’m registering on the emotional Richter scale right now, I really do want you to keep this stuff around.”

We know what you’re thinking

We know what your brain is thinking

Your brain think

s

THIS is imp

_ortant.

Your brain think

s

THIS isn’t w

orth

saving.

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xxxvi intro how to use this book

We think of a “Head First” reade

r as a learner.

Weight Normal force

θ

So what does it take to learn something? F

irst, you have to get it, then make sure you don’t forget it. It’s not about pushing f

acts into your head. Based on the latest research in cognitive science, neurobiology

, and educational psychology, learning takes a lot more than text on a pa

ge. We know what turns your brain on.

Som e of t he H e ad First le a r ning princ iple s:

M a k e it visua l. Images are far more memorable than words a

lone, and

seriously. Which would you pay more attention to

: a stimulating dinner party

Touc h t he ir e m ot ions. We now know that you

r ability to remember something

is largely dependent on its emotional content.

You remember what you care about. You remember when you feel something. No, we’re n

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you are here 4 xxxvii

the intro

Metacognition: thinking about thinking

I wonder how I can trick my brain into remembering this stuff... If you really want to learn, and you want to learn more quickly and more

deeply, pay attention to how you pay attention. Think about how you think. Learn how you learn.

Most of us did not take courses on metacognition or learning theory when we were growing up. We were expected to learn, but rarely taught to learn.

But we assume that if you’re holding this book, you really want to learn how to do physics. And you probably don’t want to spend a lot of time. If you want to use what you read in this book, you need to remember what you read. And for that, you’ve got to understand it. To get the most from this book, or any book or learning experience, take responsibility for your brain. Your brain on this

content.

The trick is to get your brain to see the new material you’re learning as Really Important. Crucial to your well-being. As important as a tiger. Otherwise, you’re in for a constant battle, with your brain doing its best to keep the new content from sticking.

So just how DO you ge t your bra in t o t re at physic s like it w a s a hungr y t ige r?

There’s the slow, tedious way, or the faster, more effective way. The

slow way is about sheer repetition. You obviously know that you are able to learn and remember even the dullest of topics if you keep pounding the same thing into your brain. With enough repetition, your brain says, “This doesn’t feel important to him, but he keeps looking at the same thing over and over and over, so I suppose it must be.”

The faster way is to do anything that increases brain activity, especially different

types of brain activity. The things on the previous page are a big part of the solution, and they’re all things that have been proven to help your brain work in your favor. For example, studies show that putting words within the pictures they describe (as opposed to somewhere else in the page, like a caption or in the body text) causes your brain to try to makes sense of how the words and picture relate, and this causes more neurons to fire. More neurons firing = more chances for your brain to get that this is something worth paying attention to, and possibly recording.

A conversational style helps because people tend to pay more attention when they perceive that they’re in a conversation, since they’re expected to follow along and hold up their end. The amazing thing is, your brain doesn’t necessarily care that the “conversation” is between you and a book! On the other hand, if the writing style is formal and dry, your brain perceives it the same way you experience being lectured to while sitting in a roomful of passive attendees. No need to stay awake.

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xxxviii intro how to use this book

Here’s what WE did:

We used pictures, because your brain is tuned for visuals, not text. As far as your brain’s concerned, a picture really is worth a thousand words. And when text and pictures work together, we embedded the text in the pictures because your brain works more effectively when the text is within the thing the text refers to, as opposed to in a caption or buried in the text somewhere.

We used redundancy, saying the same thing in different ways and with different media types, and multiple senses, to increase the chance that the content gets coded into more than one area of your brain.

We used concepts and pictures in unexpected ways because your brain is tuned for novelty, and we used pictures and ideas with at least some emotional content, because your brain is tuned to pay attention to the biochemistry of emotions. That which causes you to feel

something is more likely to be remembered, even if that feeling is nothing more than a little

humor, surprise, or interest.

We used a personalized, conversational style, because your brain is tuned to pay more attention when it believes you’re in a conversation than if it thinks you’re passively listening to a presentation. Your brain does this even when you’re reading.

We included more than 80 activities, because your brain is tuned to learn and remember more when you do things than when you read about things. And we made the exercises challenging-yet-do-able, because that’s what most peopleprefer.

We used multiple learning styles, because you might prefer step-by-step procedures, while someone else wants to understand the big picture first, and someone else just wants to see an example. But regardless of your own learning preference, everyone benefits from seeing the same content represented in multiple ways.

We include content for both sides of your brain, because the more of your brain you engage, the more likely you are to learn and remember, and the longer you can stay focused. Since working one side of the brain often means giving the other side a chance to rest, you can be more productive at learning for a longer period of time.

And we included stories and exercises that present more than one point of view,

because your brain is tuned to learn more deeply when it’s forced to make evaluations and judgments.

We included challenges, with exercises, and by asking questions that don’t always have a straight answer, because your brain is tuned to learn and remember when it has to work at something. Think about it—you can’t get your body in shape just by watching people at the gym. But we did our best to make sure that when you’re working hard, it’s on the right things. That you’re not spending one extra dendrite processing a hard-to-understand example, or parsing difficult, jargon-laden, or overly terse text.

We used people. In stories, examples, pictures, etc., because, well, because you’re a person. And your brain pays more attention to people than it does to things.

If the restoring force is proportional to the displacement, you have simple harmonic motion (abbreviated to SHM) SHM looks like circular motion from side on, and the equations for the displacement, velocity and



and the.

For a pendulum with small amplitudes, the period depends on the length and the gravitational field strength, but not on the mass.

It’s fine to use forces to analyse SHM - but you reach a point where you require

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you are here 4 xxxix

the intro

So, we did our part. The rest is up to you. These tips are a starting point; listen to your brain and figure out what works for you and what doesn’t. Try new things.

Drink w at e r. Lot s of it .

Your brain works best in a nice bath of fluid. Dehydration (which can happen before you ever feel thirsty) decreases cognitive function.

M a ke t his t he la st t hing you re a d be fore be d. Or at le a st t he la st cha lle nging t hing.

Do lot s of physic s!

The main way to learn how to do physics is by... doing physics. And that’s what you’re going to do throughout this book. We’re going to give you a lot of practice: every chapter has exercises that pose problems for you to solve. Don’t just skip over them—a lot of the learning happens when you solve the exercises. We included a solution to each exercise—don’t be afraid to peek at the solution if you get stuck! Look at the first couple of lines, then turn back and take it from there yourself ! But try to solve the problem before you look at the solution. And definitely make sure you understand the solution

before you move on to the next part of the book.

List e n t o your bra in.

Fe e l som e t hing.

Your brain needs to know that this matters. Get involved with the stories. Make up your own captions for the photos. Groaning over a bad joke is still better than feeling nothing at all.

Pay attention to whether your brain is getting overloaded. If you find yourself starting to skim the surface or forget what you just read, it’s time for a break. Once you go past a certain point, you won’t learn faster by trying to shove more in, and you might even hurt the process.

Ta lk a bout it . Out loud.

Speaking activates a different part of the brain. If you’re trying to understand something, or increase your chance of remembering it later, say it out loud. Better still, try to explain it out loud to someone else. You’ll learn more quickly, and you might uncover ideas you hadn’t known were there when you were reading about it.

Part of the learning (especially the transfer to long-term memory) happens after you put the book down. Your brain needs time on its own, to do more processing. If you put in something new during that processing time, some of what you just learned will be lost.

Re a d t he “T he re a re N o Dum b Que st ions”

That means all of them. They’re not optional sidebars—they’re part of the core content!

Don’t skip them.

Slow dow n. T he m ore you unde rst a nd, t he le ss you have t o m e m orize .

Don’t just read. Stop and think. When the book asks you a question, don’t just skip to the answer. Imagine that someone really is asking the question. The more deeply you force your brain to think, the better chance you have of learning and remembering.

Cut this out and stick it

on your refrigerator.

Here’s what YOU can do to bend

your brain into submission

Do t he exe rc ise s. Writ e your ow n not e s.

We put them in, but if we did them for you, that would be like having someone else do your workouts for you. And don’t just look at the exercises. Use a pencil. There’s plenty of evidence that physical activity while learning can increase the learning.

(42)

xl intro

how to use this book

Read Me

This is a learning experience, not a reference book. We deliberately stripped out everything that might get in the way of learning whatever it is we’re working on at that point in the book. And the first time through, you need to begin at the beginning, because the book makes assumptions about what you’ve already seen and learned.

We be gin w it h ex pe rim e nt s, m e a sure m e nt s, gra phs a nd e quat ions, t he n m ove on t o forc e s a nd e ne rgy c onse r vat ion, a nd t he n m ore a dva nc e d t opic s such a s gravit at ion a nd sim ple ha r m onic m ot ion.

It’s important to start with a firm foundation. We start out with the building blocks and tools of physics – experiments, measurements, graphs, equations – and most importantly, how to approach problems by thinking like a physicist. But this is no dry, theoretical introduction. Right from the word go, you’ll be picking up these important skills by solving problems yourself. As the book goes on, your brain is freed up to learn new concepts such as Newton’s Laws and energy conservation because you’ve already absorbed and practiced the fundamentals. By the time you reach the end of the book, you’ll even be sending people into space. We teach you what you need to know at the point where it becomes important, as that’s when it has the most value. Yes - even the math!

We c ove r t he sa m e ge ne ra l se t of t opic s t hat a re in t he

m e cha nic s se c t ions of t he AP Physic s B a nd A Leve l c ur ric ulum s

While we focus on the overall learning experience rather than exam preparation, we provide good coverage of the mechanics sections of the AP Physics B and A Level curriculums, as well as the practical side of experiments and data analysis in physics. This means that as you work your way through the topics, you gain a deeper understanding that will help you get a good grade in whatever exam you’re taking. You’ll also learn how to break down complicated problems into simpler ones that you already know how to do. This is a far more effective way of learning physics than rote memorization, as you’ll feel confident about tackling any problem even when you haven’t seen one exactly like it before. We he lp you out w it h online re sourc e s.

Our readers tell us that sometimes you need a bit of extra help, so we provide online resources, right at your fingertips. We give you an online forum where you can go to seek help, and other resources too. The starting point is

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you are here 4 xli

the intro

T he a c t ivit ie s a re N OT opt iona l.

The exercises and activities are not add-ons; they’re part of the core content of the book. Some of them are to help with memory, some are for understanding, and some will help you apply what you’ve learned. Don’t skip the exercises. The crossword puzzles are the only thing you don’t have to do, but they’re good for giving your brain a chance to think about the words and terms you’ve been learning in a different context.

T he re dunda ncy is int e nt iona l a nd im por t a nt .

One distinct difference in a Head First book is that we want you to really get it. And we want you to finish the book remembering what you’ve learned. Most reference books don’t have retention and recall as a goal, but this book is about learning, so you’ll see some of the same concepts come up more than once.

T he Bra in Pow e r exe rc ise s don’t have a nsw e rs.

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xlii intro the review team

Alice Pitt-Pitts

Bill Mietelski

Scott Donaldson

Georgia Gale Grant

Michael Lew

Catriona Lang

John Allister

_{Diane Jaquith}

Marion Lang

The technical review team

John Allister has degrees from both Oxford and Cambridge universities, including a Master’s in

Experimental and Theoretical Physics. He taught physics for 5 years and is currently training for ordination in the Church of England.

Scott Donaldson is an editor, do-it-yourselfer, and all around lover of science and mathematics, with special focus on mechanics and biology.

Georgia Gale Grant is a freelance science writer, communicator and broadcaster. She read Chemistry at Oxford University before an MSc in Science Communication at Imperial College London.

Diane Jaquith earned her Master’s degree in Physics at Wesleyan University. She taught physics, chemistry, and physical science at Durham High School, Durham, CT. She later taught chemistry at Notre Dame College and Pinkerton Academy in Derry, NH.

Catriona Lang studied singing at Birmingham Conservatoire. She currently earns her living as a singing teacher.

Marion Lang is a Classics graduate from St Andrews University who now works as a Nursery Teacher and also runs NYCoS Mini Music Makers classes. She is a member of Stirling Gaelic Choir.

Bill Mietelski is a Software Engineer and a huge Head First & Kathy Sierra fan. He plans on putting the things he learned in Head First Physics to good use while improving his golf game.

Michael Lew is an AP* Physics and Computer Science teacher at Loyola High School in Los Angeles, CA and has been teaching since 1991. In his spare time, he enjoys spending time with his wife, Britt, and his three children, Mike, Jade, and Dane.

Alice Pitt-Pitts enjoyed being a guinea pig reviewer for

Head First Physics. She also likes reading, cycling and ice cream and now knows that all of these involve energy conservation!

*AP is a registered trademark of the College Board

Technical Reviewers:

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you are here 4 xliii

the intro

The editors:

Thanks go to Catherine Nolan and Brett McLaughlin, who were editors on this project at various points, and coped admirably with the US-UK time difference. Thanks also to Mike Loukides for starting the whole thing off as far as Head First Physics was concerned.

Acknowledgments

Lou Barr

The O’Reilly team:

Thanks go to Lou Barr for turning my “wouldn’t it be dreamy if...” thoughts into reality with any artwork that’s more complicated than a line drawing. And also to Brittany Smith, who pulled off the impossible in the final stages of production. Plus Laurie Petrycki, Caitrin McCullough, Sanders Kleinfeld, Julie

Hawks, Karen Shaner and Keith McNamara.

Catherine Nolan

The distributed.physics project:

Between them, these heros and heroines got through a draft of the entire book in a single day...

Alice Pitt-Pitts, Andrew Lynn, Brian Widdas, Catriona Lang, Emma Simmons, Gareth Poulton, Graham Wood, Hazel Rostron-Wood, Jason Williams, John Vinall, Marion Lang, Peter Scandrett, Robin Lang, Roger Thetford, Stephen Swain, Tim Bannister, Tim Dickinson and Will Burt.

As well as to say:

“thanks,” this is an

experiment to test

the theory that

everyone mentioned

in a book will buy

a copy.

Brett McLaughlin

The reviewers:

Thanks to everyone on the opposite page. In particular, I’d like to mention Donald Wilke for his extremely detailed physics-specific comments and John Allister for a physics educator point of view that spanned the whole book. A lot of improvements post tech review were down to the comments of physics guinea-pigs Marion Lang, Catriona Lang and Alice Pitt-Pitts, who did a sterling job of pointing out where things could be clearer.

(46)

xliv intro safari books online

Safari® Books Online

When you see a Safari® icon on the cover of your favorite technology book that means the book is available online through the O’Reilly Network Safari Bookshelf.

(47)

this is a new chapter 1

You’re telling me that being part of the problem

is actually a good thing?

think like a physicist

1 In the beginning ...

Physics is about the world around you

and how everything in it works. As you go about your daily life, you’re doing physics all the time! But the thought of actually learning physics may sometimes feel like falling into a bottomless pit with no escape! Don’t worry... this chapter introduces how

to think like a physicist. You’ll learn to step into problems and to use your

intuition to spot patterns and ‘special points’ that make things much easier.

(48)

2 Chapter 1

U nit s

Fa lling Circ um fe re nc e

I nve rse squa re la w Ene rgy Conse r vat ion

Gra ph Ac c e le rat ion

Sc a la r I ne la st ic c ollision

Forc e Fre que ncy

Spe c ia l point s Ex pe rim e nt Pe riod

Ela st ic c ollision

Ce nt ripe t a l forc e _{We ight} _{Pe ndulum}

Sim ple H a r m onic M ot ion T im e

Angula r fre que ncy Spring

Ene rgy Gravit at iona l fie ld

Com pone nt _{Pyt ha gora s} _{Te nsion}

M om e nt um c onse r vat ion Torque Subst it ut ion _{Equat ions of m ot ion}

Pulle y Ra dia ns

I m pulse Ela st ic pot e nt ia l e ne rgy _{Be pa r t of it}

Equat ion Const a nt a c c e le rat ion N or m a l forc e Ve c t or Spe e d

Sc ie nt ific not at ion Dist a nc e Gravit at iona l pot e nt ia l e ne rgy

M e cha nic a l e ne rgy

Displa c e m e nt Trigonom e t r y Am plit ude

Angula r ve loc it y Ve loc it y Volum e Pow e r

Fric t ion

Ra dius Fre e fa ll

K ine t ic e ne rgy Fre e body dia gra m

Sym m e t r y Slope Work N e w t on’s La w s

Doe s it SU CK ? I nt e r na l e ne rgy

Are a M a ss

I don’t

get it!

Physics is the world around you

Physics is about the world around you and how stuff in the world actually works. How do you aim a cannon with no direct line of sight? How can a satellite orbit the earth without falling back down? Will you win a prize shooting ducks at the fairground? Will the Dingo catch the Emu...

All of this should be really interesting... except that opening a normal physics textbook can make you feel rather like you’ve just fallen into a bottomless pit.... welcome to the world of physics