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Head First Physics

Book Description

Wouldn't it be great if there were a physics book that showed you how things work instead of telling you how? Finally, with Head First Physics, there is. This comprehensive book takes the stress out of learning mechanics and practical physics by providing a fun and engaging experience, especially for students who "just don't get it." Head First Physics offers a format that's rich in visuals and full of activities, including pictures, illustrations, puzzles, stories, and quizzes -- a mixed-media style proven to stimulate learning and retention. One look will convince you: This isn't mere theory, this is physics brought to life through real-world scenarios, simple experiments, and hypothetical projects. Head First Physics is perfect for anyone who's intrigued by how things work in the natural world. You'll quickly discover that physics isn't a dry subject. It's all about the world we live in, encompassing everything from falling objects and speeding cars, to conservation of energy and gravity and weightlessness, and orbital behavior. This book:

  • Helps you think like a physicist so you can understand why things really work the way they do

  • Gives you relevant examples so you can fully grasp the principles before moving on to more complex concepts

  • Designed to be used as a supplement study guide for the College Board's Advanced Placement Physics B Exam

  • Introduces principles for the purpose of solving real-world problems, not memorization

  • Teaches you how to measure, observe, calculate -- and yes -- how to do the math

  • Covers scientific notation, SI units, vectors, motion, momentum conservation, Newton's Laws, energy conservation, weight and mass, gravitation and orbits, circular motion and simple harmonic motion, and much more

If "Myth Busters" and other TV programs make you curious about our physical world -- or if you're a student forced to take a physics course -- now you can pursue the subject without the dread of boredom or the fear that it will be over your head. Head First Physics comes to rescue with an innovative, engaging, and inspirational way to learn physics!

Table of Contents

  1. Dedication
  2. Special Upgrade Offer
  3. A Note Regarding Supplemental Files
  4. Advance Praise for <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="emphasis"><em>Head First Physics</em></span>
  5. Praise for other <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="emphasis"><em>Head First</em></span> academic titles academic titles
  6. Praise for the <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="emphasis"><em>Head First</em></span> Approach Approach
  7.  
  8. Author of Head First Physics
  9. How to Use this Book: Intro
    1. Who is this book for?
      1. Who should probably back away from this book?
    2. We know what you’re thinking
    3. We know what your <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="emphasis"><em>brain</em></span> is thinking is thinking
    4. Metacognition: thinking about thinking
    5. Here’s what WE did:
    6. Here’s what YOU can do to bend your brain into submission
    7. Read Me
    8. The technical review team
  10. Acknowledgments
    1. Safari<sup xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg">&#174;</sup> Books Online Books Online
  11. 1. Think Like a Physicist: In the beginning ...
    1. Physics is the world around you
    2. You can get a feel for what’s happening by <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">being</span> a part of it a part of it
      1. So - <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">could</span> you ever escape from the bottomless pit? you ever escape from the bottomless pit?
    3. Use your intuition to look for ‘special points’
    4. The center of the earth is a special point
    5. Ask yourself “What am I ALREADY doing as I reach the special point?”
    6. Where you’re at - and what happens next?
    7. Now put it all together
    8. Your Physics Toolbox
  12. 2. Making it all MEAN Something: Units and measurements
    1. It’s the best music player ever, and <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">you&#8217;re</span> part of the team! part of the team!
    2. So you get on with measuring the myPod case
    3. When the myPod case comes back from the factory...
    4. ...it’s waaay too big!
    5. There aren’t any <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">UNITS</span> on the blueprint on the blueprint
    6. You’ll use SI units in this book (and in your class)
    7. You use <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">conversion factors</span> to change units to change units
    8. You can write a conversion factor as a fraction
    9. Now you can use the conversion factor to update the blueprint
    10. You just converted the units for the entire blueprint!
    11. But there’s STILL a problem ...
    12. What to do with numbers that have waaaay too many digits to be usable
    13. How many digits of your measurements <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">look</span> significant? significant?
    14. Generally, you should round your answers to <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">three</span> significant digits significant digits
      1. You need to follow certain rules when you’re rounding answers
    15. Is it OK to round the myPod blueprint to three significant digits?
    16. You <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">ALREADY</span> intuitively rounded your original myPod measurements! intuitively rounded your original myPod measurements!
    17. Any measurement you make has an <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">error</span> (or uncertainty) associated with it (or uncertainty) associated with it
    18. The error on your original measurements should <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">propagate</span> through to your converted blueprint through to your converted blueprint
    19. Right! Time to attack the blueprint again!
    20. STOP!! Before you hit send, do your answers SUCK?!
    21. You nailed it!
    22. When you write down a measurement, you need the right number of significant digits
    23. Your Physics Toolbox
  13. 3. Scientific Notation, Area, and Volume: All numbers great and small
    1. A messy college dorm room
    2. So how long before things go really bad?
    3. Power notation helps you multiply by the same number over and over
      1. Your calculator’s power button gives you superpowers
    4. Your calculator displays big numbers using <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">scientific</span> <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">notation</span>
    5. Scientific notation uses <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">powers of 10</span> to write down long numbers to write down long numbers
    6. Scientific notation helps you with small numbers as well
    7. You’ll often need to work with area or volume
    8. Look up facts in a book (or table of information)
    9. Prefixes help with numbers outside your comfort zone
    10. Scientific notation helps you to do calculations with large and small numbers
    11. The guys have it all worked out
    12. 200,000,000 meters cubed bugs after only 16 hours is totally the wrong size of answer!
    13. Be careful converting units of area or volume
    14. So the bugs won’t take over ... unless the guys sleep in!
    15. Question Clinic: The “Converting units of area or volume” Question
    16. Your Physics Toolbox
  14. 4. Equations and Graphs: Learning the lingo
    1. The new version of the Break Neck Pizza website is nearly ready to go live ...
    2. ...but you need to work out how to give the customer their delivery time
    3. If you write the delivery time as an <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">equation</span>, you can , you can <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">see</span> what&#8217;s going on what’s going on
    4. Use <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">variables</span> to keep your equation general to keep your equation general
    5. You need to work out Alex’s cycling time
    6. When you <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">design</span> an experiment, think about what might go wrong! an experiment, think about what might go wrong!
    7. OK - time to recap where you’re at...
    8. Conduct an <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">ex</span>pp<span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">eriment</span> to find out Alex&#8217;s speed to find out Alex’s speed
      1. Here’s what happens:
    9. Write down your results... in a <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">table</span>
    10. Use the table of distances and times to work out Alex’s speed
    11. Random errors mean that results will be <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">spread</span> out out
    12. A graph is the best way of taking an average of ALL your results
    13. Use a graph to show Alex’s time for ANY distance
    14. The line on the graph is your best estimate for how long Alex takes to cycle ANY distance
    15. You can <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">see</span> Alex&#8217;s speed from the Alex’s speed from the <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">stee</span>pp<span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">ness</span> of the distance-time graph of the distance-time graph
    16. Alex’s speed is the <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">slope</span> of the distance-time graph of the distance-time graph
    17. Now work out Alex’s average speed from your graph
    18. You need an equation for Alex’s <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">time</span> to give to the web guys to give to the web guys
    19. <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">Rearrange</span> the equation to say &#8220;&#916; time = something&#8221; the equation to say “Δ time = something”
    20. Use your equation to work out the time it takes Alex to reach each house
    21. So you do a test run with the website ...
    22. So just convert the units, and you’re all set...right?
    23. Include the cooking time in your equation
    24. The Break Neck website goes live, and the customers love it!
    25. A few weeks later, you hear from Break Neck again
    26. A graph lets you <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">see the difference</span> the stop lights made the stop lights made
    27. The stop lights change Alex’s average speed
    28. Add on two minutes per stop light to give the customer a maximum delivery time ...
    29. ...the customers are extremely happy ...
    30. ...and you’re invited to the Pizza Party
    31. Question Clinic: The “Did you do what they asked you” Question
    32. Your Physics Toolbox
  15. 5. Dealing with Directions: Vectors
    1. The treasure hunt
    2. Displacement is different from distance
    3. Distance is a <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">scalar</span>; displacement is a ; displacement is a <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">vector</span>
    4. You can represent vectors using <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">arrows</span>
    5. You found the next clue...
      1. But there’s a problem ...
    6. You can add vectors in any order
    7. Well done - you’ve found the third clue!
    8. Question Clinic: The “Wheat from the chaff” Question
    9. Angles measure rotations
    10. Now you can get on with clue 3!
    11. If you can’t deal with something big, break it down into smaller parts
    12. You move onto the fourth clue...
    13. Velocity is the ‘vector version’ of speed
    14. Write units using shorthand
    15. So, on to clue 4 ...
    16. You need to allow for the <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">stream&#8217;s velocity</span> too! too!
    17. If you can find the stream’s velocity, you can figure out the velocity for the boat
    18. It takes the boat time to <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">accelerate</span> from a standing start from a standing start
    19. How do you deal with acceleration?
    20. So it’s back to the boat ...
    21. Vector, Angle, Velocity, Acceleration = WINNER!!!
    22. Your Physics Toolbox
    23. Question Clinic: The “Design an experiment” Question
  16. 6. Displacement, Velocity, and Acceleration: What’s going on?
    1. Just another day in the desert ...
    2. ...and another Dingo-Emu moment!
    3. <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">How</span> can you use what you know? can you use what you know?
    4. The cage <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">accelerates</span> as it falls as it falls
    5. ‘ Vectorize’ your equation
    6. You want an <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">instantaneous</span> velocity, not an velocity, not an <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">average</span> velocity velocity
    7. You already know how to calculate the slope of a straight line...
    8. A point on a curved line has the same slope as its <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">tangent</span>
    9. The slope of something’s velocity-time graph lets you work out its acceleration
    10. Work out the units of acceleration
    11. Success! You worked out the velocity after 2.0 s - and the cage won’t break!
    12. Now onto solve for the displacement!
    13. Your Physics Toolbox
  17. 7. Equations of motion (part 1): Playing With Equations
    1. How high should the crane be?
    2. Graphs and equations both represent the real world
    3. You’re interested in the start and end points
    4. You have an equation for the velocity - but what about the displacement?
    5. <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">See</span> the average velocity on your velocity-time graph the average velocity on your velocity-time graph
    6. Test your equations by imagining them with different numbers
    7. Calculate the cage’s displacement!
    8. You know how high the crane should be!
    9. But now the Dingo needs something more <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">general</span>
    10. A <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">substitution</span> will help will help
    11. Get rid of the variables you don’t want by making substitutions
    12. Continue making substitutions ...
    13. You did it - you derived a useful equation for the cage’s displacement!
    14. Check your equation using <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">U</span>nitsnits
    15. Check your equation by <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">t</span>rying out some extreme valuesrying out some extreme values
    16. Your equation checks out!
    17. Question Clinic: The “Substitution” Question
    18. Question Clinic: The “Units” or “Dimensional analysis” Question
    19. Think like a physicist!
    20. Your Physics Toolbox
  18. 8. Equations of Motion (Part 2): Up, up, and... back down
    1. Previously ...
    2. Now ACME has an amazing new cage launcher
    3. The acceleration due to gravity is <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">constant</span>
    4. Velocity and acceleration are in opposite <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">directions</span>, so they have opposite , so they have opposite <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">signs</span>
    5. You can use one graph to work out the <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">shapes</span> of the others of the others
    6. Is a graph of your equation the same shape as the graph you sketched?
    7. Ready to launch the cage!
      1. Your launch velocity of 5.0 m/s is definitely right!
    8. Fortunately, ACME has a rocket-powered hovercraft!
    9. You can work out a new equation by making a <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">substitution</span> for for <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="emphasis"><em>t</em></span>
    10. Multiply out the parentheses in your equation
      1. You can sort out one of the terms on the right hand side like this
    11. You have two sets of parentheses multiplied together
      1. Then you can figure out your second term on the right hand side
    12. Where you’re at with your new equation
    13. You need to <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">simplify</span> your equation by grouping the terms your equation by grouping the terms
    14. You can use your new equation to work out the stopping distance
    15. There are THREE key equations you can use when there’s constant acceleration
    16. You need to work out the launch velocity that gets the Dingo out of the Grand Canyon!
    17. The launch velocity’s right!
    18. You need to find another way of doing this problem
    19. Question Clinic: The “Sketch a graph” or “Match a graph” Question
    20. Question Clinic: The “Symmetry” and “Special points” Questions
    21. Your Physics Toolbox
  19. 9. Triangles, Trig and Trajectories: Going two-dimensional
    1. Camelot - we have a problem!
    2. How wide should you make the moat?
    3. Looks like a triangle, yeah?
    4. A scale drawing can solve problems
    5. <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">Pythagoras&#8217; Theorem</span> lets you figure out the sides quickly lets you figure out the sides quickly
    6. Sketch + shape + equation = Problem solved!
    7. You kept them out!
    8. But the attackers get smarter!
    9. Camelot ... we have ANOTHER problem!
    10. Relate your angle to an angle inside the triangle
    11. Classify similar triangles by the <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">ratios</span> of their side lengths of their side lengths
    12. Sine, cosine and tangent connect the sides and angles of a right-angled triangle
    13. How to remember which ratio is which??
    14. Calculators have sin(<span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="strong"><strong>&#952;</strong></span>), cos(), cos(<span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="strong"><strong>&#952;</strong></span>) and tan() and tan(<span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="strong"><strong>&#952;</strong></span>) tables built in) tables built in
    15. Back at the castle, everyone’s depending on you!
    16. You can know everything! *
    17. Does your answer SUCK?
    18. Uh oh. Gravity...
    19. The cannonball’s velocity and acceleration vectors point in different directions
    20. Gravity accelerates everything downwards at 9.8 m/s<sup xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg">2</sup>
    21. The horizontal component of the velocity can’t change once you’ve let go
    22. The <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">horizontal component</span> of a projectile&#8217;s velocity is constant of a projectile’s velocity is constant
    23. The same method solves both problems
    24. Question Clinic: The “Projectile” Question
    25. And so they ran away ...
    26. Question Clinic: The “Missing steps” Question
    27. Your Physics Toolbox
  20. 10. Momentum Conservation: What Newton Did
    1. The pirates be havin’ a spot o’ bother with a ghost ship ...
    2. What does the maximum range depend on?
    3. Firing at 45° maximizes your range
    4. You can’t do everything that’s <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">theoretically</span> possible - you need to be possible - you need to be <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">practical</span> too too
    5. Sieges-R-Us has a new stone cannonball, which they claim will increase the range!
    6. Massive things are more difficult to start off
    7. Massive things are more difficult to stop
    8. Newton’s First Law
    9. Mass matters
    10. A stone cannonball has a smaller mass - so it has a larger velocity. But how much larger?
    11. Here’s your lab equipment
    12. How are force, mass and velocity related?
    13. Vary only one thing at a time in your experiment
    14. Mass x velocity - momentum - is conserved
    15. A greater force acting over the same amount of time gives a greater change in momentum
    16. Write momentum conservation as an <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">equation</span>
    17. Momentum conservation and Newton’s Third Law are equivalent
    18. You’ve calculated the stone cannonball’s velocity...
    19. ...but you want the new <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">range!</span>
    20. Use <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">proportion</span> to work out the new range to work out the new range
    21. You solved the pirates’ problem!
    22. Question Clinic: The “Proportion” Question (often multiple choice)
    23. Your Physics Toolbox
  21. 11. Weight and the normal force: Forces for courses
    1. WeightBotchers are at it again!
    2. Is it really possible to lose weight instantly?!
    3. Scales work by compressing or stretching a spring
    4. Mass is a measurement of “stuff”
    5. Weight is a force
    6. The relationship between force and mass involves <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">momentum</span>
    7. If the object’s mass is constant, F<sub xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg">net</sub> = = <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="emphasis"><em>ma</em></span>
    8. The scales measure the support force
    9. Now you can debunk the machine!
    10. The machine reduces the support force
    11. Force pairs help you check your work
    12. You debunked WeightBotchers!
    13. But WeightBotchers are back!
    14. A surface can only exert a force perpendicular (or normal) to it
    15. When you slide downhill, there’s zero <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">perpendicular</span> acceleration acceleration
    16. Use parallel and perpendicular force components to deal with a slope
    17. Another fake busted!
    18. Question Clinic: The “Free body diagram” Question
    19. Question Clinic: The “Free body diagram” Question
    20. Your Physics Toolbox
  22. 12. Using forces, momentum, friction and impulse: Getting on with it
    1. It’s ... SimFootball!
    2. Momentum is conserved in a collision
    3. But the collision might be at an angle
    4. A triangle with no right angles is awkward
    5. Use component vectors to create some right-angled triangles
    6. The programmer includes 2D momentum conservation ...
    7. ...but the players keep on sliding for ever!
    8. In real life, the force of friction is present
    9. Friction depends on the types of surfaces that are interacting
    10. Friction depends on the normal force
    11. Be careful when you calculate the normal force
    12. You’re ready to use friction in the game!
    13. Including friction stops the players from sliding forever!
    14. The sliding players are fine - but the tire drag is causing problems
    15. Using components for the tire drag works!
    16. Question Clinic: The “Friction” Question
    17. How does kicking a football work?
    18. FΔt is called impulse
    19. The game’s great - but there’s just been a spec change!
    20. The strength of the moon’s gravitational field is lower then the Earth’s
    21. For added realism, sometimes the players should slip
    22. You can change only direction horizontally on a flat surface because of friction
    23. The game is brilliant, and going to X-Force rocks!
    24. Newton’s Laws give you awesome powers
    25. Your Physics Toolbox
  23. 13. Torque and Work: Getting a lift
    1. Half the kingdom to anyone who can lift the sword in the stone ...
    2. Can physics help you to lift a heavy object?
    3. Use a <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">lever</span> to turn a small force into a larger force to turn a small force into a larger force
    4. Do an experiment to determine where to position the fulcrum
    5. Zero net <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">torque</span> causes the lever to balance causes the lever to balance
    6. Use torque to lift the sword and the stone!
    7. Question Clinic: The “Two equations, two unknowns” Question
    8. So you lift the sword and stone with the lever ...
    9. ...but they don’t go high enough!
    10. You can’t get something for nothing
    11. When you move an object against a force, you’re doing work
    12. The work you need to do a job = force x displacement
    13. Which method involves the least amount of work?
    14. Work has units of Joules
    15. Energy is the capacity that something has to do work
    16. Lifting stones is like <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">transferring</span> energy from one store to another energy from one store to another
    17. Energy conservation helps you to solve problems with differences in height
    18. One of our stackable stones is missing ...
    19. Will energy conservation save the day?
    20. You need to do work against <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">friction</span> as well as against gravity as well as against gravity
    21. Doing work against friction increases internal energy
    22. Heating increases internal energy
    23. It’s impossible to be 100% efficient
    24. Your Physics Toolbox
  24. 14. Energy Conservation: Making your life easier
    1. The ultimate bobsled experience
    2. Forces and component vectors solve the first part ...
    3. ...but the second part doesn’t have a uniform slope
    4. A moving object has kinetic energy
    5. The kinetic energy is related to the velocity
    6. Calculate the velocity using energy conservation and the change in height
    7. You’ve used energy conservation to solve the second part
    8. In the third part, you have to apply a force to stop a moving object
    9. Putting on the brake does work on the track
    10. Doing work against friction increases the internal energy
    11. Energy conservation helps you to do complicated problems in a simpler way
    12. There’s a <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">practical</span> difference between momentum and kinetic energy difference between momentum and kinetic energy
    13. Question Clinic: The “Show that” Question
    14. Question Clinic: The “Energy transfer” Question
    15. After the roaring success of SimFootball, it’s time for SimPool
      1. Reusing the old code makes the pool balls stick together!
    16. Momentum conservation will solve an inelastic collision problem
    17. You need a second equation for an elastic collision
    18. Energy conservation gives you the second equation that you need!
    19. Factoring involves putting in parentheses
    20. You can deal with elastic collisions now
    21. In an elastic collision, the relative velocity reverses
    22. The pool ball collisions work!
    23. There’s a gravity-defying trick shot to sort out ...
    24. Where is the problem with the programmer’s reasoning?
    25. The initial collision is inelastic - so mechanical energy isn’t conserved
    26. Use momentum conservation for the inelastic part
    27. Question Clinic: The “Ballistic pendulum” Question
    28. Your Physics Toolbox
  25. 15. Tension, Pulleys and Problem Solving: Changing direction
    1. It’s a bird... it’s plane...
    2. ...no, it’s... a guy on a skateboard?!
    3. Always look for something familiar
    4. Michael and the stack accelerate at the same rate
    5. Use tension to tackle the problem
    6. Look at the big picture as well as the parts
    7. But the day before the competition ...
    8. Using energy conservation is simpler than using forces
    9. There goes that skateboard...
    10. Your Physics Toolbox
  26. 16. Circular Motion (Part 1): From α to ω
    1. Limber up for the Kentucky Hamster Derby
    2. You can revolutionize the hamsters’ training
    3. Thinking through different approaches helps
    4. A circle’s radius and circumference are linked by <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="emphasis"><em><span class="strong"><strong>&#928;</strong></span></em></span>
    5. Convert from linear distance to revolutions
    6. Convert the linear speeds into Hertz
    7. So you set up the machine ...
    8. ...but the wheel turns too slowly!
    9. Try some numbers to work out how things relate to each other
      1. What if you set the motor to ‘1.0’?
      2. What if the wheel goes at 1.0 Hz?
    10. The units on the motor are radians per second
    11. Convert frequency to angular frequency
    12. The hamster trainer is complete!
    13. A couple of weeks later ...
    14. You can increase the (linear) speed by increasing the wheel’s radius
    15. Question Clinic: The “Angular quantities” Question
    16. Your Physics Toolbox
  27. 17. Circular Motion (Part 2) Staying on track
    1. Houston ... we have a problem
    2. When you’re in freefall, objects appear to float beside you
    3. What’s the astronaut missing, compared to when he’s on Earth?
    4. Can you mimic the contact force you feel on Earth?
    5. <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">Accelerating</span> the space station allows you to experience a contact force the space station allows you to experience a contact force
    6. You can only go in a circle because of a <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">centripetal</span> force force
    7. Centripetal force acts towards the center of the circle
    8. The astronaut experiences a contact force when you <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">rotate</span> the space station the space station
    9. What affects the size of centripetal force?
    10. Spot the equation for the centripetal acceleration
    11. Give the astronauts a centripetal force
    12. The astronauts want as much floor space as possible
    13. Here, the floor space is the area of a cylinder’s curved surface
    14. If you work out the volume, you can calculate the astronauts’ floor space
    15. Let’s test the space station...
      1. Can’t cope with rotation
      2. Apple falls straight while space station rotates
      3. Head and feet at different radii
    16. Fewer uncomfortable things happen with the 100 m radius space station
    17. You’ve sorted out the space station design!
    18. Question Clinic: The “Centripetal force” Question
    19. Back to the track!
    20. The bobsled needs to turn a corner
    21. Angling the track gives the normal force a horizontal component
    22. When you slide downhill, there’s no <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">perpendicular</span> acceleration acceleration
    23. When you turn a corner, there’s no <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">vertical</span> acceleration acceleration
    24. How to deal with an object on a slope
    25. Banking the track works ...
    26. ...but now they want it to loop-the-loop!
    27. The “support force” (normal force or tension force) required for a vertical circle varies
    28. Any force that acts towards the center of the circle can provide a centripetal force
    29. How fast does the bobsled need to go?
    30. Question Clinic: The “Banked curve” Question
    31. Question Clinic: The “Vertical circle” Question
    32. Your Physics Toolbox
  28. 18. Gravitation and Orbits: Getting away from it all
    1. Party planners, a big event, and lots of cheese
    2. What <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">length</span> should the cocktail sticks be? should the cocktail sticks be?
    3. The cheese globe is a <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">sphere</span>
    4. The surface area of the sphere is the <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">same</span> as the surface area of the cheese as the surface area of the cheese
    5. Let there be cheese...
    6. ...but there are gaps in the globe!
    7. The party’s on!
    8. To infinity - and beyond!
    9. Earth’s gravitational force on you becomes <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">weaker</span> as you go further away as you go further away
    10. Gravitation is an <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">inverse</span> <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">s</span>qq<span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">uare</span> <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">law</span>
    11. Now you can calculate the force on the spaceship at <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">any</span> distance from the Earth distance from the Earth
    12. The potential energy is the area under the force-displacement graph
    13. If U = 0 at infinity, the equation works for any star or planet
    14. Use energy conservation to calculate the astronaut’s escape velocity
    15. We need to keep up with our astronaut
    16. The centripetal force is provided by gravity
    17. With the comms satellites in place, it’s Pluto (and beyond)
    18. Question Clinic: The “gravitational force = centripetal force” Question
    19. Your Physics Toolbox
  29. 19. Oscillations (Part 1): Round and round
    1. Welcome to the fair!
    2. Reproduce the duck on the display
    3. The screen for the game is <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">TWO</span>--<span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">DIMENSIONAL</span>
    4. So we know what the duck does...
    5. ...but where exactly is the duck?
    6. Any time you’re dealing with a component vector, try to spot a right-angled triangle
    7. Let’s show Jane the display
    8. The second player sees the <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">x</span>--<span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">com</span>pp<span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">onent</span> of the duck&#8217;s displacement of the duck’s displacement
    9. We need a wider definition of cosine, too
    10. sine and cosine are <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">related</span> to each other to each other
    11. Let the games begin!
    12. Jane’s got another request: What’s the duck’s <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">velocity</span> from each player&#8217;s point of view? from each player’s point of view?
    13. Get the <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">shape</span> of the velocity-time graph from the of the velocity-time graph from the <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">slope</span> of the displacement-time graph of the displacement-time graph
    14. The game is complete!
    15. Your Physics Toolbox
  30. 20. Oscillations (Part 2): Springs ‘n’ swings
    1. Get rocking, not talking
    2. The plant rocker needs to work for three different masses of plant
    3. A <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">spring</span> will produce regular oscillations will produce regular oscillations
    4. Displacement from equilibrium and strength of spring affect the force
    5. A mass on a spring moves like a side-on view of circular motion
    6. A mass on a spring moves with <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:pls="http://www.w3.org/2005/01/pronunciation-lexicon" xmlns:ssml="http://www.w3.org/2001/10/synthesis" xmlns:svg="http://www.w3.org/2000/svg" class="underline">simple harmonic motion</span>
    7. Simple harmonic motion is sinusoidal
    8. Work out constants by comparing a situation-specific equation with a standard equation
      1. Look at the amplitude
      2. Look at the argument of the cosine
    9. Question Clinic: The “This equation is like that one” Question
    10. You rock! Or at least Anne’s plants do
    11. But Anne forgot to mention someting ...
    12. The plants rock - and you rule!
    13. But now the plant rocker’s frequency has changed ...
    14. The frequency of a horizontal spring depends on the mass
    15. Will using a vertical spring make a difference?
    16. A pendulum swings with simple harmonic motion
    17. What does the frequency of a pendulum depend on?
    18. The pendulum design works!
    19. Question Clinic: The “Vertical spring” Question
    20. Question Clinic: The “How does this depend on that” Question
    21. Your Physics Toolbox
  31. 21. Think Like a Physicist: It’s the final chapter
    1. You’ve come a long way!
    2. Now you can finish off the globe
    3. The round-trip looks like simple harmonic motion
    4. But what time does the round-trip take?
    5. You can treat the Earth like a sphere and a shell
    6. The net force from the shell is zero
    7. The force is proportional to the displacement, so your trip is SHM
    8. Question Clinic: The “Equation you’ve never seen before” Question
    9. You know your average speed - but what’s your top speed?
    10. Circular motion from side on looks like simple harmonic motion
    11. You can do (just about) anything!
  32. A. Leftovers: The top 6 things (that we didn’t cover before, but are covering now)
    1. #1 Equation of a straight line graph, y = mx + c
    2. #2 Displacement is the area under the velocity-time graph
    3. #3 Torque on a bridge
    4. #4 Power
    5. #5 Lots of practice questions
    6. #6 Exam tips
  33. B. Equation Table: Point of Reference
    1. Mechanics equation table
  34. Index
  35. About the Author
  36. Special Upgrade Offer
  37. Copyright