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460 664.4 463.9 485.6 408.9 511.1 1022.2 511.1 511.1 511.1 0 0 0 0 0 0 0 0 0 0 0 Jan 11, 2023 OpenStax. >> This is for small angles only. 323.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 569.4 323.4 323.4 295.1 826.4 501.7 501.7 826.4 795.8 752.1 767.4 811.1 722.6 693.1 833.5 795.8 382.6 How does adding pennies to the pendulum in the Great Clock help to keep it accurate? WebAnalytic solution to the pendulum equation for a given initial conditions and Exact solution for the nonlinear pendulum (also here). >> moving objects have kinetic energy. /Subtype/Type1 <> How about some rhetorical questions to finish things off? endobj /BaseFont/EKGGBL+CMR6 743.3 743.3 613.3 306.7 514.4 306.7 511.1 306.7 306.7 511.1 460 460 511.1 460 306.7 Problem (12): If the frequency of a 69-cm-long pendulum is 0.601 Hz, what is the value of the acceleration of gravity $g$ at that location? That's a question that's best left to a professional statistician. We recommend using a endobj You may not have seen this method before. 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 Students calculate the potential energy of the pendulum and predict how fast it will travel. /FirstChar 33 481.5 675.9 643.5 870.4 643.5 643.5 546.3 611.1 1222.2 611.1 611.1 611.1 0 0 0 0 593.8 500 562.5 1125 562.5 562.5 562.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 /Widths[351.8 611.1 1000 611.1 1000 935.2 351.8 481.5 481.5 611.1 935.2 351.8 416.7 Find its (a) frequency, (b) time period. Creative Commons Attribution License What is the acceleration of gravity at that location? 777.8 694.4 666.7 750 722.2 777.8 722.2 777.8 0 0 722.2 583.3 555.6 555.6 833.3 833.3 WebStudents are encouraged to use their own programming skills to solve problems. We begin by defining the displacement to be the arc length ss. 481.5 675.9 643.5 870.4 643.5 643.5 546.3 611.1 1222.2 611.1 611.1 611.1 0 0 0 0 stream 1444.4 555.6 1000 1444.4 472.2 472.2 527.8 527.8 527.8 527.8 666.7 666.7 1000 1000 >> not harmonic or non-sinusoidal) response of a simple pendulum undergoing moderate- to large-amplitude oscillations. They attached a metal cube to a length of string and let it swing freely from a horizontal clamp. Solution: first find the period of this pendulum on Mars, then using relation $f=1/T$ find its frequency. can be important in geological exploration; for example, a map of gg over large geographical regions aids the study of plate tectonics and helps in the search for oil fields and large mineral deposits. 8 0 obj 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 627.2 817.8 766.7 692.2 664.4 743.3 715.6 500 500 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 625 833.3 WebThe solution in Eq. << 6 0 obj How long of a simple pendulum must have there to produce a period of $2\,{\rm s}$. To Find: Potential energy at extreme point = E P =? Although adding pennies to the Great Clock changes its weight (by which we assume the Daily Mail meant its mass) this is not a factor that affects the period of a pendulum (simple or physical). /BaseFont/OMHVCS+CMR8 g When is expressed in radians, the arc length in a circle is related to its radius (LL in this instance) by: For small angles, then, the expression for the restoring force is: where the force constant is given by k=mg/Lk=mg/L and the displacement is given by x=sx=s. WebSimple Pendulum Calculator is a free online tool that displays the time period of a given simple. In this case, the period $T$ and frequency $f$ are found by the following formula \[T=2\pi\sqrt{\frac{\ell}{g}}\ , \ f=\frac{1}{T}\] As you can see, the period and frequency of a pendulum are independent of the mass hanged from it. Set up a graph of period vs. length and fit the data to a square root curve. /BaseFont/VLJFRF+CMMI8 799.2 642.3 942 770.7 799.4 699.4 799.4 756.5 571 742.3 770.7 770.7 1056.2 770.7 endstream WebSimple pendulum definition, a hypothetical apparatus consisting of a point mass suspended from a weightless, frictionless thread whose length is constant, the motion of the body about the string being periodic and, if the angle of deviation from the original equilibrium position is small, representing simple harmonic motion (distinguished from physical pendulum). WebWalking up and down a mountain. 1999-2023, Rice University. Will it gain or lose time during this movement? The equation of period of the simple pendulum : T = period, g = acceleration due to gravity, l = length of cord. << /Pages 45 0 R /Type /Catalog >> /FirstChar 33 /Widths[660.7 490.6 632.1 882.1 544.1 388.9 692.4 1062.5 1062.5 1062.5 1062.5 295.1 Problem (6): A pendulum, whose bob has a mass of $2\,{\rm g}$, is observed to complete 50 cycles in 40 seconds. We can solve T=2LgT=2Lg for gg, assuming only that the angle of deflection is less than 1515. Problem (1): In a simple pendulum, how much the length of it must be changed to triple its period? endobj Problem (2): Find the length of a pendulum that has a period of 3 seconds then find its frequency. 35 0 obj Homogeneous first-order linear partial differential equation: /Type/Font Note how close this is to one meter. The two blocks have different capacity of absorption of heat energy. . 20 0 obj The rope of the simple pendulum made from nylon. Get There. How to solve class 9 physics Problems with Solution from simple pendulum chapter? /Widths[1000 500 500 1000 1000 1000 777.8 1000 1000 611.1 611.1 1000 1000 1000 777.8 The heart of the timekeeping mechanism is a 310kg, 4.4m long steel and zinc pendulum. 12 0 obj Begin by calculating the period of a simple pendulum whose length is 4.4m. The period you just calculated would not be appropriate for a clock of this stature. 611.1 798.5 656.8 526.5 771.4 527.8 718.7 594.9 844.5 544.5 677.8 762 689.7 1200.9 826.4 295.1 531.3] Look at the equation below. /Name/F9 H /Type/Font We can discern one half the smallest division so DVVV= ()05 01 005.. .= VV V= D ()385 005.. 4. 777.8 777.8 1000 1000 777.8 777.8 1000 777.8] Even simple pendulum clocks can be finely adjusted and accurate. Page Created: 7/11/2021. Web1 Hamiltonian formalism for the double pendulum (10 points) Consider a double pendulum that consists of two massless rods of length l1 and l2 with masses m1 and m2 attached to their ends. i.e. The quantities below that do not impact the period of the simple pendulum are.. B. length of cord and acceleration due to gravity. WebSimple Pendulum Problems and Formula for High Schools. First method: Start with the equation for the period of a simple pendulum. 750 758.5 714.7 827.9 738.2 643.1 786.2 831.3 439.6 554.5 849.3 680.6 970.1 803.5 /Type/Font Websome mistakes made by physics teachers who retake models texts to solve the pendulum problem, and finally, we propose the right solution for the problem fashioned as on Tipler-Mosca text (2010). 24/7 Live Expert. This is why length and period are given to five digits in this example. 1277.8 811.1 811.1 875 875 666.7 666.7 666.7 666.7 666.7 666.7 888.9 888.9 888.9 /FontDescriptor 41 0 R 843.3 507.9 569.4 815.5 877 569.4 1013.9 1136.9 877 323.4 569.4] /BaseFont/JMXGPL+CMR10 /BaseFont/HMYHLY+CMSY10 PHET energy forms and changes simulation worksheet to accompany simulation. 3.5 Pendulum period 72 2009-02-10 19:40:05 UTC / rev 4d4a39156f1e Even if the analysis of the conical pendulum is simple, how is it relevant to the motion of a one-dimensional pendulum? /FontDescriptor 20 0 R when the pendulum is again travelling in the same direction as the initial motion. 833.3 1444.4 1277.8 555.6 1111.1 1111.1 1111.1 1111.1 1111.1 944.4 1277.8 555.6 1000 Now for the mathematically difficult question. Find its PE at the extreme point. The initial frequency of the simple pendulum : The frequency of the simple pendulum is twice the initial frequency : For the final frequency to be doubled, the length of the pendulum should be changed to 0.25 meters. This PDF provides a full solution to the problem. /Widths[622.5 466.3 591.4 828.1 517 362.8 654.2 1000 1000 1000 1000 277.8 277.8 500 384.3 611.1 675.9 351.8 384.3 643.5 351.8 1000 675.9 611.1 675.9 643.5 481.5 488 /FirstChar 33 24 0 obj Since gravity varies with location, however, this standard could only be set by building a pendulum at a location where gravity was exactly equal to the standard value something that is effectively impossible. Arc length and sector area worksheet (with answer key) Find the arc length. 21 0 obj By how method we can speed up the motion of this pendulum? 896.3 896.3 740.7 351.8 611.1 351.8 611.1 351.8 351.8 611.1 675.9 546.3 675.9 546.3 /FirstChar 33 endobj An object is suspended from one end of a cord and then perform a simple harmonic motion with a frequency of 0.5 Hertz. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 753.7 1000 935.2 831.5 500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 <> /BaseFont/LQOJHA+CMR7 If displacement from equilibrium is very small, then the pendulum of length $\ell$ approximate simple harmonic motion. WebThe simple pendulum system has a single particle with position vector r = (x,y,z). 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 562.5 312.5 312.5 342.6 24 0 obj 597.2 736.1 736.1 527.8 527.8 583.3 583.3 583.3 583.3 750 750 750 750 1044.4 1044.4 Attach a small object of high density to the end of the string (for example, a metal nut or a car key). 42 0 obj >> 492.9 510.4 505.6 612.3 361.7 429.7 553.2 317.1 939.8 644.7 513.5 534.8 474.4 479.5 WebView Potential_and_Kinetic_Energy_Brainpop. 624.1 928.7 753.7 1090.7 896.3 935.2 818.5 935.2 883.3 675.9 870.4 896.3 896.3 1220.4 <> ollB;% !JA6Avls,/vqnpPw}o@g `FW[StFb s%EbOq#!!!h#']y\1FKW6 /Name/F7 The length of the cord of the simple pendulum (l) = 1 meter, Wanted: determine the length of rope if the frequency is twice the initial frequency. If this doesn't solve the problem, visit our Support Center . I think it's 9.802m/s2, but that's not what the problem is about. 777.8 777.8 1000 1000 777.8 777.8 1000 777.8] /Subtype/Type1 Weboscillation or swing of the pendulum. The displacement ss is directly proportional to . The angular frequency formula (10) shows that the angular frequency depends on the parameter k used to indicate the stiffness of the spring and mass of the oscillation body. Knowing Physics 1 First Semester Review Sheet, Page 2. 593.8 500 562.5 1125 562.5 562.5 562.5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 877 0 0 815.5 677.6 646.8 646.8 970.2 970.2 323.4 354.2 569.4 569.4 569.4 569.4 569.4 << Tell me where you see mass. /FirstChar 33 endobj 875 531.3 531.3 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 A 1.75kg particle moves as function of time as follows: x = 4cos(1.33t+/5) where distance is measured in metres and time in seconds. by /FontDescriptor 29 0 R % Solution: The period and length of a pendulum are related as below \begin{align*} T&=2\pi\sqrt{\frac{\ell}{g}} \\\\3&=2\pi\sqrt{\frac{\ell}{9.8}}\\\\\frac{3}{2\pi}&=\sqrt{\frac{\ell}{9.8}} \\\\\frac{9}{4\pi^2}&=\frac{\ell}{9.8}\\\\\Rightarrow \ell&=9.8\times\left(\frac{9}{4\pi^2}\right)\\\\&=2.23\quad{\rm m}\end{align*} The frequency and periods of oscillations in a simple pendulum are related as $f=1/T$. The most popular choice for the measure of central tendency is probably the mean (gbar). >> stream The relationship between frequency and period is. Then, we displace it from its equilibrium as small as possible and release it. Bonus solutions: Start with the equation for the period of a simple pendulum. An instructor's manual is available from the authors. A "seconds pendulum" has a half period of one second. endobj << WebA simple pendulum is defined to have an object that has a small mass, also known as the pendulum bob, which is suspended from a light wire or string, such as shown in Figure 16.13. 687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.8 562.5 625 312.5 What is the cause of the discrepancy between your answers to parts i and ii? Notice how length is one of the symbols. WebAuthor: ANA Subject: Set #4 Created Date: 11/19/2001 3:08:22 PM N*nL;5 3AwSc%_4AF.7jM3^)W? /Widths[342.6 581 937.5 562.5 937.5 875 312.5 437.5 437.5 562.5 875 312.5 375 312.5 What is the generally accepted value for gravity where the students conducted their experiment? 277.8 500] they are also just known as dowsing charts . Consider a geologist that uses a pendulum of length $35\,{\rm cm}$ and frequency of 0.841 Hz at a specific place on the Earth. /FontDescriptor 26 0 R WebSo lets start with our Simple Pendulum problems for class 9. /Type/Font WebPeriod and Frequency of a Simple Pendulum: Class Work 27. /FontDescriptor 8 0 R 33 0 obj 0.5 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 295.1 N xnO=ll pmlkxQ(ao?7 f7|Y6:t{qOBe>`f (d;akrkCz7x/e|+v7}Ax^G>G8]S n%[SMf#lxqS> :1|%8pv(H1nb M_Z}vn_b{u= ~; sp AHs!X ,c\zn3p_>/3s]Ec]|>?KNpq n(Jh!c~D:a?FY29hAy&\/|rp-FgGk+[Io\)?gt8.Qs#pxv[PVfn=x6QM[ W3*5"OcZn\G B$ XGdO[. endobj Wanted: Determine the period (T) of the pendulum if the length of cord (l) is four times the initial length. Solution: This configuration makes a pendulum. /FirstChar 33 /BaseFont/CNOXNS+CMR10 Solution: endobj 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 277.8 777.8 472.2 472.2 777.8 491.3 383.7 615.2 517.4 762.5 598.1 525.2 494.2 349.5 400.2 673.4 531.3 295.1 0 0 This method isn't graphical, but I'm going to display the results on a graph just to be consistent. endobj 306.7 766.7 511.1 511.1 766.7 743.3 703.9 715.6 755 678.3 652.8 773.6 743.3 385.6 endobj <> stream 61) Two simple pendulums A and B have equal length, but their bobs weigh 50 gf and l00 gf respectively. /Name/F3 There are two constraints: it can oscillate in the (x,y) plane, and it is always at a xed distance from the suspension point. /Name/F8 /Type/Font Webpendulum is sensitive to the length of the string and the acceleration due to gravity. /LastChar 196 Two pendulums with the same length of its cord, but the mass of the second pendulum is four times the mass of the first pendulum. /Name/F12 1000 1000 1055.6 1055.6 1055.6 777.8 666.7 666.7 450 450 450 450 777.8 777.8 0 0 <>/ExtGState<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> /LastChar 196 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 642.9 885.4 806.2 736.8 Example 2 Figure 2 shows a simple pendulum consisting of a string of length r and a bob of mass m that is attached to a support of mass M. The support moves without friction on the horizontal plane. 0 0 0 0 0 0 0 0 0 0 0 0 675.9 937.5 875 787 750 879.6 812.5 875 812.5 875 0 0 812.5 750 758.5 714.7 827.9 738.2 643.1 786.2 831.3 439.6 554.5 849.3 680.6 970.1 803.5 The motion of the cart is restrained by a spring of spring constant k and a dashpot constant c; and the angle of the pendulum is restrained by a torsional spring of Based on the equation above, can conclude that mass does not affect the frequency of the simple pendulum. If f1 is the frequency of the first pendulum and f2 is the frequency of the second pendulum, then determine the relationship between f1 and f2. <> WebSOLUTION: Scale reads VV= 385. << For the precision of the approximation Now, if we can show that the restoring force is directly proportional to the displacement, then we have a simple harmonic oscillator. /BaseFont/SNEJKL+CMBX12 endstream (Keep every digit your calculator gives you. 285.5 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 285.5 285.5 542.4 542.4 456.8 513.9 1027.8 513.9 513.9 513.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 For the next question you are given the angle at the centre, 98 degrees, and the arc length, 10cm. 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 777.8 500 777.8 500 530.9 x|TE?~fn6 @B&$& Xb"K`^@@ << endobj What is the period on Earth of a pendulum with a length of 2.4 m? 324.7 531.3 531.3 531.3 531.3 531.3 795.8 472.2 531.3 767.4 826.4 531.3 958.7 1076.8 One of the authors (M. S.) has been teaching the Introductory Physics course to freshmen since Fall 2007. 314.8 787 524.7 524.7 787 763 722.5 734.6 775 696.3 670.1 794.1 763 395.7 538.9 789.2 >> What is the answer supposed to be? 8.1 Pendulum experiments Activity 1 Your intuitive ideas To begin your investigation you will need to set up a simple pendulum as shown in the diagram. Our mission is to improve educational access and learning for everyone. We will then give the method proper justication. /Name/F3 Determine the comparison of the frequency of the first pendulum to the second pendulum. 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 Projectile motion problems and answers Problem (1): A person kicks a ball with an initial velocity of 15\, {\rm m/s} 15m/s at an angle of 37 above the horizontal (neglect the air resistance). 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 663.6 885.4 826.4 736.8 Websector-area-and-arc-length-answer-key 1/6 Downloaded from accreditation. endobj 783.4 872.8 823.4 619.8 708.3 654.8 0 0 816.7 682.4 596.2 547.3 470.1 429.5 467 533.2 We will present our new method by rst stating its rules (without any justication) and showing that they somehow end up magically giving the correct answer. 14 0 obj The problem said to use the numbers given and determine g. We did that. /BaseFont/EUKAKP+CMR8 The length of the cord of the first pendulum (l1) = 1, The length of cord of the second pendulum (l2) = 0.4 (l1) = 0.4 (1) = 0.4, Acceleration due to the gravity of the first pendulum (g1) = 1, Acceleration due to gravity of the second pendulum (g2) = 0.9 (1) = 0.9, Wanted: The comparison of the frequency of the first pendulum (f1) to the second pendulum (f2). There are two constraints: it can oscillate in the (x,y) plane, and it is always at a xed distance from the suspension point. The time taken for one complete oscillation is called the period. /FirstChar 33 In Figure 3.3 we draw the nal phase line by itself. 343.8 593.8 312.5 937.5 625 562.5 625 593.8 459.5 443.8 437.5 625 593.8 812.5 593.8 /Type/Font xc```b``>6A WebEnergy of the Pendulum The pendulum only has gravitational potential energy, as gravity is the only force that does any work. Instead of an infinitesimally small mass at the end, there's a finite (but concentrated) lump of material. What is the acceleration due to gravity in a region where a simple pendulum having a length 75.000 cm has a period of 1.7357 s? That means length does affect period. /Filter[/FlateDecode] The comparison of the frequency of the first pendulum (f1) to the second pendulum (f2) : 2. /FirstChar 33 Compute g repeatedly, then compute some basic one-variable statistics. Current Index to Journals in Education - 1993 << 500 500 611.1 500 277.8 833.3 750 833.3 416.7 666.7 666.7 777.8 777.8 444.4 444.4 351.8 935.2 578.7 578.7 935.2 896.3 850.9 870.4 915.7 818.5 786.1 941.7 896.3 442.6 /BaseFont/NLTARL+CMTI10 3 0 obj 545.5 825.4 663.6 972.9 795.8 826.4 722.6 826.4 781.6 590.3 767.4 795.8 795.8 1091 /LastChar 196 <> >> Understanding the problem This involves, for example, understanding the process involved in the motion of simple pendulum. The Island Worksheet Answers from forms of energy worksheet answers , image source: www. In this case, this ball would have the greatest kinetic energy because it has the greatest speed. 21 0 obj /Widths[285.5 513.9 856.5 513.9 856.5 799.4 285.5 399.7 399.7 513.9 799.4 285.5 342.6 We are asked to find gg given the period TT and the length LL of a pendulum. Pendulum . The individuals who are preparing for Physics GRE Subject, AP, SAT, ACTexams in physics can make the most of this collection. 7195c96ec29f4f908a055dd536dcacf9, ab097e1fccc34cffaac2689838e277d9 Our mission is to improve educational access and In this problem has been said that the pendulum clock moves too slowly so its time period is too large. Divide this into the number of seconds in 30days. Thus, the period is \[T=\frac{1}{f}=\frac{1}{1.25\,{\rm Hz}}=0.8\,{\rm s}\] Each pendulum hovers 2 cm above the floor. /Type/Font /Name/F5 WebSimple Pendulum Calculator is a free online tool that displays the time period of a given simple. 495.7 376.2 612.3 619.8 639.2 522.3 467 610.1 544.1 607.2 471.5 576.4 631.6 659.7 Boundedness of solutions ; Spring problems . 324.7 531.3 590.3 295.1 324.7 560.8 295.1 885.4 590.3 531.3 590.3 560.8 414.1 419.1 708.3 795.8 767.4 826.4 767.4 826.4 0 0 767.4 619.8 590.3 590.3 885.4 885.4 295.1 The worksheet has a simple fill-in-the-blanks activity that will help the child think about the concept of energy and identify the right answers. 571 285.5 314 542.4 285.5 856.5 571 513.9 571 542.4 402 405.4 399.7 571 542.4 742.3 460 511.1 306.7 306.7 460 255.6 817.8 562.2 511.1 511.1 460 421.7 408.9 332.2 536.7 A cycle is one complete oscillation. When we discuss damping in Section 1.2, we will nd that the motion is somewhat sinusoidal, but with an important modication. /LastChar 196 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 /Subtype/Type1 (7) describes simple harmonic motion, where x(t) is a simple sinusoidal function of time. Pendulum Practice Problems: Answer on a separate sheet of paper! WebAustin Community College District | Start Here. /Subtype/Type1 All of us are familiar with the simple pendulum. << Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . 44 0 obj How about its frequency? endstream Solutions to the simple pendulum problem One justification to study the problem of the simple pendulum is that this may seem very basic but its /LastChar 196 << %PDF-1.5 Why does this method really work; that is, what does adding pennies near the top of the pendulum change about the pendulum? /Widths[622.5 466.3 591.4 828.1 517 362.8 654.2 1000 1000 1000 1000 277.8 277.8 500 /LastChar 196 Calculate gg. Restart your browser. stream are licensed under a, Introduction: The Nature of Science and Physics, Introduction to Science and the Realm of Physics, Physical Quantities, and Units, Accuracy, Precision, and Significant Figures, Introduction to One-Dimensional Kinematics, Motion Equations for Constant Acceleration in One Dimension, Problem-Solving Basics for One-Dimensional Kinematics, Graphical Analysis of One-Dimensional Motion, Introduction to Two-Dimensional Kinematics, Kinematics in Two Dimensions: An Introduction, Vector Addition and Subtraction: Graphical Methods, Vector Addition and Subtraction: Analytical Methods, Dynamics: Force and Newton's Laws of Motion, Introduction to Dynamics: Newtons Laws of Motion, Newtons Second Law of Motion: Concept of a System, Newtons Third Law of Motion: Symmetry in Forces, Normal, Tension, and Other Examples of Forces, Further Applications of Newtons Laws of Motion, Extended Topic: The Four Basic ForcesAn Introduction, Further Applications of Newton's Laws: Friction, Drag, and Elasticity, Introduction: Further Applications of Newtons Laws, Introduction to Uniform Circular Motion and Gravitation, Fictitious Forces and Non-inertial Frames: The Coriolis Force, Satellites and Keplers Laws: An Argument for Simplicity, Introduction to Work, Energy, and Energy Resources, Kinetic Energy and the Work-Energy Theorem, Introduction to Linear Momentum and Collisions, Collisions of Point Masses in Two Dimensions, Applications of Statics, Including Problem-Solving Strategies, Introduction to Rotational Motion and Angular Momentum, Dynamics of Rotational Motion: Rotational Inertia, Rotational Kinetic Energy: Work and Energy Revisited, Collisions of Extended Bodies in Two Dimensions, Gyroscopic Effects: Vector Aspects of Angular Momentum, Variation of Pressure with Depth in a Fluid, Gauge Pressure, Absolute Pressure, and Pressure Measurement, Cohesion and Adhesion in Liquids: Surface Tension and Capillary Action, Fluid Dynamics and Its Biological and Medical Applications, Introduction to Fluid Dynamics and Its Biological and Medical Applications, The Most General Applications of Bernoullis Equation, Viscosity and Laminar Flow; Poiseuilles Law, Molecular Transport Phenomena: Diffusion, Osmosis, and Related Processes, Temperature, Kinetic Theory, and the Gas Laws, Introduction to Temperature, Kinetic Theory, and the Gas Laws, Kinetic Theory: Atomic and Molecular Explanation of Pressure and Temperature, Introduction to Heat and Heat Transfer Methods, The First Law of Thermodynamics and Some Simple Processes, Introduction to the Second Law of Thermodynamics: Heat Engines and Their Efficiency, Carnots Perfect Heat Engine: The Second Law of Thermodynamics Restated, Applications of Thermodynamics: Heat Pumps and Refrigerators, Entropy and the Second Law of Thermodynamics: Disorder and the Unavailability of Energy, Statistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation, Introduction to Oscillatory Motion and Waves, Hookes Law: Stress and Strain Revisited, Simple Harmonic Motion: A Special Periodic Motion, Energy and the Simple Harmonic Oscillator, Uniform Circular Motion and Simple Harmonic Motion, Speed of Sound, Frequency, and Wavelength, Sound Interference and Resonance: Standing Waves in Air Columns, Introduction to Electric Charge and Electric Field, Static Electricity and Charge: Conservation of Charge, Electric Field: Concept of a Field Revisited, Conductors and Electric Fields in Static Equilibrium, Introduction to Electric Potential and Electric Energy, Electric Potential Energy: Potential Difference, Electric Potential in a Uniform Electric Field, Electrical Potential Due to a Point Charge, Electric Current, Resistance, and Ohm's Law, Introduction to Electric Current, Resistance, and Ohm's Law, Ohms Law: Resistance and Simple Circuits, Alternating Current versus Direct Current, Introduction to Circuits and DC Instruments, DC Circuits Containing Resistors and Capacitors, Magnetic Field Strength: Force on a Moving Charge in a Magnetic Field, Force on a Moving Charge in a Magnetic Field: Examples and Applications, Magnetic Force on a Current-Carrying Conductor, Torque on a Current Loop: Motors and Meters, Magnetic Fields Produced by Currents: Amperes Law, Magnetic Force between Two Parallel Conductors, Electromagnetic Induction, AC Circuits, and Electrical Technologies, Introduction to Electromagnetic Induction, AC Circuits and Electrical Technologies, Faradays Law of Induction: Lenzs Law, Maxwells Equations: Electromagnetic Waves Predicted and Observed, Introduction to Vision and Optical Instruments, Limits of Resolution: The Rayleigh Criterion, *Extended Topic* Microscopy Enhanced by the Wave Characteristics of Light, Photon Energies and the Electromagnetic Spectrum, Probability: The Heisenberg Uncertainty Principle, Discovery of the Parts of the Atom: Electrons and Nuclei, Applications of Atomic Excitations and De-Excitations, The Wave Nature of Matter Causes Quantization, Patterns in Spectra Reveal More Quantization, Introduction to Radioactivity and Nuclear Physics, Introduction to Applications of Nuclear Physics, The Yukawa Particle and the Heisenberg Uncertainty Principle Revisited, Particles, Patterns, and Conservation Laws, A simple pendulum has a small-diameter bob and a string that has a very small mass but is strong enough not to stretch appreciably.