Calculus-Based Physics
a Free Physics Textbook
by Jeffrey W. Schnick, Ph.D.
Physics Department
Saint Anselm College

 cbPhysics Home Page 1st Semester Downloads 2nd Semester Downloads About the Book Off-Site Resources What's New?* This work is licensed under a Creative Commons License. Specification of Manner of Attribution

What's New?

##### A Brief History of the Calculus-Based Physics Web Site

 2/17/2014 Added the Feynman Lectures link to the list of offsite resources. 9/26/2013 I have converted all the problem solution videos to H.264 MP4 format and uploaded all the solutions to YouTube.  I added links to the YouTube playlist on the solutions pages of this web site. 8/23/2012 Reformatted SAC102 video solutions to H.264 MP4 format 8/28/08 Minor corrections of typos to Volume I.  New version is cbphysicsIA18. 3/24/08 Corrected some typos in the 2nd Semester SAC problems.  The current version is of the problems document is SACProblemsIIa14. 3/12/08 Correction to page 188 of Volume I Chapter 21: Changed amplitude to "square of amplitude".  New version of Volume II is cbPhysicsIIb24. 3/01/08 Removed the circle from each of the integral signs for the magnetic flux through a loop in Chapter 18 of Volume II.  New version of Volume II is cbPhysicsIIb23. 2/28/08 Added computer algebra section to off-site resources page. 2/21/08 Corrected solution to SAC215-4.  Many thanks to Christopher Benoit. 1/30/08 Edited solutions dealing with electric potential to effect change of using phi instead of V for electric potential in 2nd semester SAC problems. 1/14/08 Updated the 2nd semester formula sheet accessible from the 2nd Semester Downloads page. 1/9/08 Volume II of book: Corrected some minor typos.  Added "one kind of charge" footnote--thanks to John Denker for his insights on that.  Changed notation so that phi (instead of V) represents electric potential.  Am still using V for electric potential difference.  So, V = Delta phi.  12/2/07 Corrected solution to SAC134-3 11/18/07 Added solution to SAC131-6. 11/17/07 Minor change to problem statement for SAC132-6.  Replaced the soltution that had been posted for SAC132-6 with the actual solution to that problem. 9/3/07 Correction to solution to SAC103-4.  (Added "reference level.") 8/19/07 Fine-tuned the 1st semester SAC problems.  Avoided calling a variable a function, made all force variable names F_subscript.  Changed the problem involving the Beck Centripetal Force apparatus to make the problem a statics problem.  The document is now named SACsproblemsIa12. 8/15/07 I made a lot of minor edits to Volume I, and changed the notation for forces such that every force is represented by an F with a subscript.  I also changed the wording to reflect something that John Denker reminded me of on phys-l, namely that in an expression such as v= v_0+at, v is not a function of t, rather, t and v are both variables and v is what you get when you evaluate a function, e.g. if you call the function g, v=g(t)= v_0+at.  This version of Volume I of the book is the one available at LuLu where it is called the green edition. 8/06/07 Added Data Analysis and Uncertainty Calculations section to the Offsite Resources page. 8/04/07 On the Off-Site Resources web page: removed dead links to The College Physics Mathematics Pretest of H.T. Hudson and T.L. O'Kuma. Added link to textbookrevolution.org.  I had that link on the Off-Site Resources page before but the site vanished from the internet for awhile--it is back. 6/9/07 Corrected error in example 4-1 on page 23 of Volume I.  I had substituted the wrong value for m1.  Many thanks to Kyle Markham for pointing out this mistake. 6/8/07 Added information on what students are expected to turn in for each of the SAC problems that students are expected to solve using numerical methods on a spreadsheet. 6/7/07 Changed drop distance for problem SAC106A-4 and changed "acceleration" to "angular acceleration" in problem SAC117-6. 4/22/07  In Volume II of the book, I corrected the equations in the discussion of Gauss's Law for the magnetic field--where I should have had an infinitesimal area element I had an infinitesimal length element.  Page 322, changed "distance" to "square of the distance" in writing about r^2.  (Many thanks to Alex Macomber for pointing out the latter error.)  The new version of Volume II is cbPhysicsIIb21. 4/22/07  In Volume II of book:  The page break between pages 287 and 288 occurred at a bad spot.  I fixed that.  Changed "spherical" to "closed" in characterizing an egg-shaped surface on page 297.  On page 302, removed note about depicted Gaussian surface looking like a circle since diagram has been improved to make it look like a spherical shell. The new version of Volume II is cbPhysicsIIb20. 4/14/07  Edited ray tracing diagram problem statements in SAC II problems to specify use of 1:1 scale.  Made minor cosmetic edits to other SAC II problem statements as well.  New version is SACProblemsIIa10. 4/13/07  Corrected wavelength value for "blue" light on page 239.  (Thanks to Tom Dahlberg and Ben Doucette.) 4/8/07  The textbookrevolution web site is being moved to a new host.  For now, the link is dead so I removed it from the cbphysics "What's New" web page. 3/31/07  In Volume II, made some minor edits on page 238, made page number correction to page 205 (thanks to Katherine Thibodeau), and (thanks to Brendan Sweeny) added page headers on pages in chapter 22 that were missing them.  New version of Volume II is cbphysicsIIb19. 3/25/07  SAC problem 223-3 became 223a-4 and I created a new SAC problem 223-3.  I posted a solution to the latter and renamed the solution file sac223n3.asf to sac223an4.asf and bundled the latter with the rest of the sac223a solutions.  The new version of the 2nd semester problem set is SACProblemsIIa9. 3/10/07  Made following edits to volume 2:    Page 146: (3rd to last line): Change "from which the extend" to "from which they extend"    Page 159: last sentence: change "decreasing" to "increasing"    Page 171: Change "Source" to "source" Many thanks to Amanda Chatterton, Alex Macomber, and Ben Streeter! New version of volume 2 is cbphysicsIIb17. Also, have finished adding quizzes to Calculus-Based Physics II Learners Moodle course. 3/2/07 Refined SAC128 problem 4.  The new version of the 2nd semester SAC Problems is sacProbsIIa8. 2/25/07 Added solution to SAC215-4 to 2nd Semester Solutions.  Corrected subscript on page 20 (thanks to Amanda Chatterton) and removed extra word from chapter 17 (thanks to Alex Macomber) of Volume II.  New version is cbphysicsIIb16. 2/17/07 Correction to problem statement for SAC212-3.  New version of SAC Problems is sacProbsIIa7. 2/12/07 Changed seat of EMF values in SAC211-2 and 211-3 back to original values to conform with posted solutions.  New version of SAC Problems is sacProbsIIa6. 1/28/07 Minor change to SAC 205-2 solution (put arrow over symbol used to represent final velocity). 1/27/07 Minor changes to 2nd semester formula sheet--new version is formulaIIa3. 12/31/06 Published cbphysicsIIb15 to Lulu.com . 12/31/06 Minor changes to Volume II--new version is cbphysicsIIb15. 12/30/06 Volume II: Shortened chapters 18, 19, 20, and 22 and made some cosmetic changes. The new version is cbphysicsIIb14. 12/22/06 Dr. David Banach of the Saint Anselm College Philosophy Department set up a cbphysics Moodle server on the Linux host he runs out of his home.  I have started setting up Moodle courses using the resources at this site. The Moodle courses currently under construction are at www.cbphysics.com/moodle . 12/21/06 Over the last 3 months I have built up the solutions to 1st semester SAC physics problems.  In particular, I have added 28 new screen capture movie solutions.  In some cases these were used to replace old screen capture movie solutions and old scanned pencil on paper solutions; in other cases they are solutions to problems for which no solution had previously been posted.  I have also made some fairly minor alterations to the 1st semester problems sets--mostly minor edits to individual problems but I found one problem statement that was in the wrong set; I replaced it with a new problem and made it a "new" last problem in the existing set to which it belonged--where it should have been in the first place. 10/22/06 Minor edits to the 1st semester SAC problems.  New version is SACproblemsIa5.  I have added several solutions to 1st Semester Downloads / Solutions to SAC Problems. 9/09/06 Volume I p29:changed "no transfer of momentum" to "no transfer of angular momentum."  New vers: cbphysicsIa14. 9/03/06 Added the Merry-Go-Round video to the 1st semester downloads. 9/03/06 Minor edits have been done to chapters 1-4 of volume I since the last update (current version is cbphysicsIa13).  The solutions to 1st semester SAC problems have been updated.  In particular, the WinCam exe files have been replaced with ASF files.  The WinCam movies can now be viewed under the Mac and Linux operating systems.  (They can still be viewed under Windows as well.)  The QuickTime and avi 1st semester solution files have been replaced (to reduce file size improve resolution). 8/23/06 Changed avgWithErr and gaussEP to allow users to format rows, columns and cells without having to turn protection off.  Current versions are avgWithErrA2.xls and gauseEPv3.xls . 8/22/06 Made improvements to the average with error spreadsheet and the Gaussian error propagation spreadsheet based on suggestions by Kathleen Shartzer, Laboratory Instructor at Saint Anselm College.  The biggest change was to protect some cells to prevent accidental changing of values in them.  (It is easy for the user to remove protection: Tools--Protection--Unprotect Worksheet.)  Current versions are avgWithErrA2.xls and gaussEPv3.xls . 8/20/06 Updated the Off-Site Resources web page.  Added links to Donald Simanek's Physics Abused web page and the NIST web site. 8/19/06 Replaced the Gaussian error propagation spreadsheets with a single spreadsheet gaussEPv2.xls.zip good for 1 to 6 variables.  Added Average with Error spreadsheet AvgWithErrA1.xls to the math resources web page.  It is for calculating the mean and standard deviation of a set of values entered by the user. 8/18/06 Posted revised versions of error propagation spreadsheets. 1varErrPropA2.xls to 6varErrPropA2.xls . 8/17/06 Posted revised versions of error propagation spreadsheets. 1varErrPropA1.xls to 6varErrPropA1.xls . 8/14/06 Added missing section break between chapters 5 and 6 of volume I and republished to LuLu.com.  New version is cbphysicsIa12. 8/10/06 Added links to error propagation spreadsheets to the math resources web page.  Each spreadsheet is used to find the mean and standard deviation of a quantity that is a function of other quantities for which the means and standard deviations are known.  A Monte Carlo method is used to generate a column of 1000 values corresponding to a Gaussian distribution for each argument of the function and histogram of each set of 1000 values is displayed.  The values are used to calculate 1000 values of the function and a statistical analysis of that set of values is done to determine a mean and standard deviation.  A histogram of the 1000 values of the function is also displayed. 8/8/06 The screen capture with audio physics problem solution videos for the first semester have been converted to asf format (as opposed to exe format).  Now students can watch (and listen to) the movies using operating systems other than WindowsTM.  I replace the old wmv and mov files with scans of paper solutions because of the low quality and large file size of the wmv and mov movies.  This and the conversions greatly reduced the overall size of the 1st semester solutions package. 8/8/06 Minor edits to volume 1.  (p28:emboldened decimal point in "32.0"; p90: inserted comma after "chains"; p91: "string" to "rope" in 2 places; p99: subscript spacing in F_x.) New version is cbphysicsIa11. 8/3/06 Wherever, in volume II, I had written about the flow of current, I replaced such text with the "flow of charge," or, as in "the direction of the flow of current," I struck "flow of" so that, for instance, the example given would read the "direction of the current."  (Charge flows.  Current does not.)  The new version of volume 2 is cbphysicsIIb14. 7/30/06 Published current version of volume I (cbphysicsIa10) to LuLu with a light blue cover--I called it the blue edition. 7/29/06 Many thanks to Dr. Leigh Palmer, Prof. Emeritus, Simon Fraser University, who pointed out that my statement (in chapter 23) that the principle of conservation of energy is the central, most important, concept in physics was "over the top."  I agree!  I added "in the opinion of the author" to the sentence.  The new version of volume 1 is cbphysicsIa10. 7/21/06 Minor edits to chapters 20-34,36,37 of volume 1.  Changes to chapter 35.  New version of volume 1 is cbphysicsIa9. 7/16/06 Minor edits to chapters 3-19 of volume 1.  New version of volume 1 is cbphysicsIa8. 7/9/06 Minor edits to volume 1, mostly to chapter 2.  New version of volume 1 is cbphysicsIa7. 7/1/06 Added question sets for chapters 27, 28, and 29 to the 2nd semester class questions.  The current versions of the files containing the second semester class questions are: ClassQuestionsIIa5.pdf and ClassQuestionsIIa5.ppt.zip . 6/8/06 Added links to Physics Documents by John S. Denker and the PHYS-L listserve to the Offsite resources page.  Added links to the The College Physics Mathematics Pretest of H.T. Hudson and T.L. O'Kuma 6/4/06 Fixed a link error pointed out to me by Eric Ostlund.  My add3vectors.xls link on the Math Resources page was pointing to add2vectors.xls by mistake.  It now points to add3vectors.xls as intended.  This is the first mistake pointed out to me by someone from the general public and I am most grateful to Eric Ostlund for his random act of kindness. 6/3/06 Made numerous edits, mostly cosmetic, to the 1st-semester SAC Problems. The current versions of the files containing them are: SACprobsIa2.pdf and SACprobsIa2.doc.zip . 6/2/06 Added the pre-calculus math videos and the calculus ScreenCam movies to 1st Semester Downloads under Math Resources.  Added links to add2vectors and add3vectors spreadsheets to the Math Resources web page. 5/29/06 Made numerous edits, mostly cosmetic, to the second-semester class questions. The current versions of the files containing them are: ClassQuestionsIIa4.pdf and ClassQuestionsIIa4.ppt.zip . 5/26/06 Moved the math resource links that were on the 1st Semester Downloads page to a separate Math Resources page and, on the 1st semester downloads page, I replaced the links to individual math resources with a link to that one page. 5/21/06 Made numerous edits, mostly cosmetic, to the first semester class questions. The current versions of the files containing them are: ClassQuestionsIa3.pdf and ClassQuestionsIa3.ppt.zip . 5/16/06 I zipped up all the 2nd semester class questions and posted the zip file and a pdf file of all the 2nd semester class questions to the 2nd semester downloads page. I removed the html page with the links to the individual 2nd semester class question files. 5/11/06 Changed the artwork in the Gauss's Law chapters (Calculus-Based Physics II chapters 35 and 36) to give 3D Gaussian surfaces, electric fields, and charge distributions a 3D look. The (old) 2D look caused some confusion about the nature of a closed surface. New version of volume 2 is cbphysicsIIb13.doc. 5/6/06 The diagrams in problem SAC 211-5 looked like double exposures in the pdf version of the 2nd Semester SAC Problems. I made changes to the WordTM version of the 2nd Semester SAC problems and the 2nd Semester SAC problems in Random Order and generated the corresponding pdf files. All the new versions have now been uploaded to this site. 5/5/06 Corrected a typographical error found by Katherine Coit and one found by Cristian Costescu. Both errors were near the end of Calculus-Based Physics II (roughly chapter 32 and chapter 36). At the time of this post, Katherine and Cristian are students in my Classical Physics course. The current version of volume II is cbphysicsIIb12. Added 2nd semester class questions for ch 34 and 37. 4/29/06 Fixed link to 2nd semester solutions on the Downloads II page. (It was set to the 1st semester solutions.) 4/28/06 Added a misconception preamble to Volume II Chapter 32 (Gauss's Law). Added some 3D effects to diagrams in chapter 32 and text emphasis that Gaussian surfaces enclose 3D volumes of space. The new version of volume 2 is cbphysicsIIb11 (replacing cbphysicsIIb10). Added second semester lecture 35 class questions. 4/23/06 On the "Offsite Resources" web page: Added a link to the University of Minnesota Physics Education Research and Development web page. 4/22/06 Added more 2nd semester class questions. I also added some more 1st semester class questions. The new compressed file ClassQuestionsIa2.ppt.zip includes all the old 1st semester class questions as well as the new ones. Added the "About the Book" page to the web site and posted the "Why I Wrote the Book and Why I Released it for Free" document. Eliminated javascript from the web pages. Also, I noticed that the sample WinCamTM (executable files) would no longer download and play. Instead, upon clicking on one of them, one would get a file not found message despite the fact that the file was there. I assume this is the result of a recent security update to Microsoft Internet ExplorerTM. I compressed the sample WinCamTM files. Now the user has to download and unzip a WinCamTM executable file to watch a WinCamTM movie. I revised the instructions accordingly. 4/15/06 Uploaded an updated version of the 2nd semester SAC problems. The update represents many minor edits made during the Spring 2006 semester. Most of them were cosmetic but there were some corrections, and, a couple of new problems were added as well. Embedded fonts other than common system fonts in the textbook word files so that folks can edit the WordTM files without having to install the physics and GoLoSymbols fonts. Eliminated some of the text from the home page. 4/08/06 Added more 2nd semester class questions. 4/2/06 Added the link to Donald Simanek's physics documents and links to my list of offsite research. What a resource! 3/31/06 Added more 2nd semester class questions and I embedded fonts in all the 2nd semester class questions. I created a new zip file ClassQuestionsIIa2.ppt.zip of the class question files (with fonts embedded), but, I did not create a new pdf version of the class questions--I plan to wait until the end of the semester to do that. I embedded fonts in the 1st semester class questions too. The files in ClassQuestionsIa1.ppt.zip now include the fonts. 3/24/06 Added more 2nd semester class questions. 3/18/06 Starting with cbphysicsIIb9: Added equation numbers to 3 equations in chapter 19 Induction, Transformers, and Generators. On page 185, changed "The total magnetic at point P field" to "The total magnetic field at point P" to correct word order error. (Thank you Jamie Vaughn!) On page 200: put the E in the equation relating the intensity of light to the amplitude of the electric field oscillations in italics. (It was in the normal font.) On page 13, corrected spelling of Calculus and put book title "Calculus-Based Physics" in italics. On page 211, two lines above diagram, changed "the the" to "the." (Thank you Cristian Costescu!) Resulting version is cbphysicsIIb10. 3/10/06 Made minor edits to chapters 30-37 of Calculus-Based Physics II (now cbphysicsIIb9). 3/8/06 Made minor edits to chapters 28-37 of Calculus-Based Physics II (now cbphysicsIIb8). I included some of the steps that I had intentionally left out of the solution to the second example problem in chapter 32. I decided to include them so that the reader would not have to flip back to chapter 30 to understand the solution; and; in order to avoid conveying the impression that it would be okay for a student, in solving a homework problem, to start with an intermediate result from a sample problem rather than to start from "first principles." This made chapter 32 one page longer than it was. In chapter 30, in several cases, I made a copy of a diagram or equation that was on one page, on the next page, to reduce the amount of flip-back that the reader had to do in referring back to earlier diagrams and equations. This lengthened chapter 30 by one page. I also removed the equation numbers from the steps in the solutions to the example problems in chapter 30. In chapter 37 I corrected some glaring errors in the tables of the very last page of the book. 3/4/06 Made minor edits to chapters 25-27 of Calculus-Based Physics II (now cbphysicsIIb7). 3/3/06 Added more 2nd semester class questions. 2/25/06 Made minor edits to chapter 11 (thanks to Katharine Coit and Kevin Bersell), chapter 17 (thanks to Cristian Costescu), and chapters 22-24 of Calculus-Based Physics II (now cbphysicsIIb6). 2/18/06 Made minor edits to chapters 19-21 of Calculus-Based Physics II (now cbphysicsIIb5). 2/10/06 Made minor edits to Calculus-Based Physics I including the addition of information on power units in chapter 25 as recommended by Katharine Coit and Kevin Bersell, students in my calculus-based physics course. 1/27/06 Created a new page entitled "Additional Class Questions" under 2nd Semester Downloads and started posting the new class question power point slides that I am creating for the current semester to that page. Any old question sets that I revise this semester will be posted there too (so there will probably be some redundancy with the question sets in the zip file). The plan is to incorporate the new question sets in the pdf and zip files at the end of this semester and remove the "Additional Class Questions" page at that time. 1/17/06 Combined chapters 32 and 33 into 1 chapter thus reducing the number of chapters to 37. 1/8/06 Replaced cbphysicsIIa1 (Volume 2 of the book) with cbphysicsIb1. Added chapter 38. Shortened chapter 20. Made minor corrections to chapter 1. 12/31/05 Made cbphysicsIIb1 (Calculus-Based Physics II) available as a paperback black-and-white book at lulu.com at the cost of production, namely \$11.44, which is less than what it would cost me to make a photocopy of the book. 12/31/05 Made cbphysicsIa5 (Calculus-Based Physics I) available as a paperback black-and-white book at lulu.com at the cost of production, namely \$9.88, which is less than what it would cost me to make a photocopy of the book. 12/31/05 Replaced cbphysicsIa4 (Volume 1 of the book) with cbphysicsIa5. (Minor corrections.) 12/27/05 Added 2nd-semester Class Questions (Microsoft Power PointTM slides and pdf version of same) to 2nd Semester Downloads. 12/23/05 Added 1st-semester Class Questions (Microsoft PowerPointTM slides and pdf version of same) to 1st Semester Downloads. 12/11/05 Replaced cbphysicsIa3 (Volume 1 of the book) with cbphysicsIa4. (Eliminated 1 erratum. It was pointed out to me by Jamie Vaughn, a student in my calculus-based physics course.) To update your copy of cbphysicsIa3 to cbphysicaIa4, replace pages 1 and 78. 12/09/05 Replaced cbphysicsIa2 (Volume 1 of the book) with cbphysicsIa3. (Eliminated 4 errata, 3 of which were pointed out to me by Cristian Costescu, a student in my calculus-based physics course.) To update your hard copy of cbphysicsIa2 to cbphysicaIa3, replace pages 1, 80, and 264 from cbphysicsIa2 with pages 1, 80, and 264, respectively, from cbphysicsIa3. 12/08/05 Added links to professor Hunt's Physics Tutorials and Socratic Problem Solutions. 12/08/05 Added pdf "printouts" of the on-line Blackboard quizzes to both 1st semester and 2nd semester downloads. 11/26/05 Added fonts and 1st semester formula sheet to 1st semester downloads. 11/25/05 Added "What's New." 11/25/05 Replaced cbphysicsIa1 (Volume 1 of the book) with cbphysicsIa2. cbphysicsIa2 implements an estimated 20-30 minor edits correcting errors (10 of which were pointed out to me by my students!) uncovered through use of the book during the Fall 2005 semester at Saint Anselm College. These corrections would be listed as errata in a traditionally-published book. 10/25/05 Added Math Handouts to 1st semester downloads. 11/24/05 Added Solutions to 2nd Semester Physics Problems 11/20/05 Added Off-Site Resources page. 11/14/05 Released Calculus-Based Physics (version a revision 1) and ancillary materials under the Creative Commons License .