Find its PE at the extreme point. Calculate the period of a simple pendulum whose length is 4.4m in London where the local gravity is 9.81m/s2. Which answer is the best answer? WebPhysics 1 Lab Manual1Objectives: The main objective of this lab is to determine the acceleration due to gravity in the lab with a simple pendulum. /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 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 By shortening the pendulum's length, the period is also reduced, speeding up the pendulum's motion. /BaseFont/JMXGPL+CMR10 /Type/Font /Type/Font /Name/F8 /Subtype/Type1 <> /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 (a) Find the frequency (b) the period and (d) its length. /Name/F5 742.3 799.4 0 0 742.3 599.5 571 571 856.5 856.5 285.5 314 513.9 513.9 513.9 513.9 That means length does affect period. /FontDescriptor 23 0 R /Subtype/Type1 B ased on the above formula, can conclude the length of the rod (l) and the acceleration of gravity (g) impact the period of the simple pendulum. This result is interesting because of its simplicity. 1. 4 0 obj /Contents 21 0 R endstream endstream Solution: The period of a simple pendulum is related to the acceleration of gravity as below \begin{align*} T&=2\pi\sqrt{\frac{\ell}{g}}\\\\ 2&=2\pi\sqrt{\frac{\ell}{1.625}}\\\\ (1/\pi)^2 &= \left(\sqrt{\frac{\ell}{1.625}}\right)^2 \\\\ \Rightarrow \ell&=\frac{1.625}{\pi^2}\\\\&=0.17\quad {\rm m}\end{align*} Therefore, a pendulum of length about 17 cm would have a period of 2 s on the moon. not harmonic or non-sinusoidal) response of a simple pendulum undergoing moderate- to large-amplitude oscillations. 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 To Find: Potential energy at extreme point = E P =? /FontDescriptor 20 0 R /BaseFont/UTOXGI+CMTI10 /Name/F12 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. Solution; Find the maximum and minimum values of \(f\left( {x,y} \right) = 8{x^2} - 2y\) subject to the constraint \({x^2} + {y^2} = 1\). /FontDescriptor 26 0 R A classroom full of students performed a simple pendulum experiment. 513.9 770.7 456.8 513.9 742.3 799.4 513.9 927.8 1042 799.4 285.5 513.9] 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 Want to cite, share, or modify this book? /FontDescriptor 14 0 R /BaseFont/AQLCPT+CMEX10 xc```b``>6A 0 0 0 0 0 0 0 615.3 833.3 762.8 694.4 742.4 831.3 779.9 583.3 666.7 612.2 0 0 772.4 15 0 obj 666.7 666.7 666.7 666.7 611.1 611.1 444.4 444.4 444.4 444.4 500 500 388.9 388.9 277.8 /BaseFont/EUKAKP+CMR8 /Subtype/Type1 0 0 0 0 0 0 0 615.3 833.3 762.8 694.4 742.4 831.3 779.9 583.3 666.7 612.2 0 0 772.4 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). 875 531.3 531.3 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 295.1 Physics 1 First Semester Review Sheet, Page 2. By the end of this section, you will be able to: Pendulums are in common usage. The short way F /Filter[/FlateDecode] If, is the frequency of the first pendulum and, is the frequency of the second pendulum, then determine the relationship between, Based on the equation above, can conclude that, ased on the above formula, can conclude the length of the, (l) and the acceleration of gravity (g) impact the period of, determine the length of rope if the frequency is twice the initial frequency. /Subtype/Type1 /Type/Font 812.5 875 562.5 1018.5 1143.5 875 312.5 562.5] endobj Play with one or two pendulums and discover how the period of a simple pendulum depends on the length of the string, the mass of the pendulum bob, and the amplitude of the swing. 384.3 611.1 611.1 611.1 611.1 611.1 896.3 546.3 611.1 870.4 935.2 611.1 1077.8 1207.4 2.8.The motion occurs in a vertical plane and is driven by a gravitational force. (*
!>~I33gf. 935.2 351.8 611.1] Pendulum . /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 << 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 endstream /Name/F6 777.8 777.8 1000 500 500 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 777.8 /FirstChar 33 /FThHh!nmoF;TSooevBFN""(+7IcQX.0:Pl@Hs (@Kqd(9)\ (jX A "seconds pendulum" has a half period of one second. Websimple-pendulum.txt. <> stream /Subtype/Type1 /Name/F4 A classroom full of students performed a simple pendulum experiment. 314.8 472.2 262.3 839.5 577.2 524.7 524.7 472.2 432.9 419.8 341.1 550.9 472.2 682.1 24 0 obj endobj Substitute known values into the new equation: If you are redistributing all or part of this book in a print format, 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 In trying to determine if we have a simple harmonic oscillator, we should note that for small angles (less than about 1515), sinsin(sinsin and differ by about 1% or less at smaller angles). >> then you must include on every digital page view the following attribution: Use the information below to generate a citation. In Figure 3.3 we draw the nal phase line by itself. endobj They attached a metal cube to a length of string and let it swing freely from a horizontal clamp. 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 Thus, the period is \[T=\frac{1}{f}=\frac{1}{1.25\,{\rm Hz}}=0.8\,{\rm s}\] /BaseFont/LQOJHA+CMR7 /FontDescriptor 35 0 R [4.28 s] 4. <> << 795.8 795.8 649.3 295.1 531.3 295.1 531.3 295.1 295.1 531.3 590.3 472.2 590.3 472.2 There are two constraints: it can oscillate in the (x,y) plane, and it is always at a xed distance from the suspension point. << 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 >> A 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. >> endobj endobj 388.9 1000 1000 416.7 528.6 429.2 432.8 520.5 465.6 489.6 477 576.2 344.5 411.8 520.6 593.8 500 562.5 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 >> This is the video that cover the section 7. 277.8 500] 10 0 obj << 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 then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a digital format, /BaseFont/JFGNAF+CMMI10 Put these information into the equation of frequency of pendulum and solve for the unknown $g$ as below \begin{align*} g&=(2\pi f)^2 \ell \\&=(2\pi\times 0.841)^2(0.35)\\&=9.780\quad {\rm m/s^2}\end{align*}. Two simple pendulums are in two different places. 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? This PDF provides a full solution to the problem. 5 0 obj /LastChar 196 805.5 896.3 870.4 935.2 870.4 935.2 0 0 870.4 736.1 703.7 703.7 1055.5 1055.5 351.8 We recommend using a Divide this into the number of seconds in 30days. 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 /Widths[323.4 569.4 938.5 569.4 938.5 877 323.4 446.4 446.4 569.4 877 323.4 384.9 820.5 796.1 695.6 816.7 847.5 605.6 544.6 625.8 612.8 987.8 713.3 668.3 724.7 666.7 Note the dependence of TT on gg. WebClass 11 Physics NCERT Solutions for Chapter 14 Oscillations. Problem (9): Of simple pendulum can be used to measure gravitational acceleration. /BaseFont/EKBGWV+CMR6 656.3 625 625 937.5 937.5 312.5 343.8 562.5 562.5 562.5 562.5 562.5 849.5 500 574.1 WebThe simple pendulum is another mechanical system that moves in an oscillatory motion. Students calculate the potential energy of the pendulum and predict how fast it will travel. Projecting the two-dimensional motion onto a screen produces one-dimensional pendulum motion, so the period of the two-dimensional motion is the same stream
/LastChar 196 stream 675.9 1067.1 879.6 844.9 768.5 844.9 839.1 625 782.4 864.6 849.5 1162 849.5 849.5 WebWalking up and down a mountain. endobj Restart your browser. 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 Snake's velocity was constant, but not his speedD. WebSo lets start with our Simple Pendulum problems for class 9. 61) Two simple pendulums A and B have equal length, but their bobs weigh 50 gf and l00 gf respectively. Pendulum Practice Problems: Answer on a separate sheet of paper! /FontDescriptor 38 0 R Solution: (a) the number of complete cycles $N$ in a specific time interval $t$ is defined as the frequency $f$ of an oscillatory system or \[f=\frac{N}{t}\] Therefore, the frequency of this pendulum is calculated as \[f=\frac{50}{40\,{\rm s}}=1.25\, {\rm Hz}\] << endobj 6.1 The Euler-Lagrange equations Here is the procedure. /Subtype/Type1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 642.3 856.5 799.4 713.6 685.2 770.7 742.3 799.4 Simple pendulum ; Solution of pendulum equation ; Period of pendulum ; Real pendulum ; Driven pendulum ; Rocking pendulum ; Pumping swing ; Dyer model ; Electric circuits; 35 0 obj Half of this is what determines the amount of time lost when this pendulum is used as a time keeping device in its new location. It takes one second for it to go out (tick) and another second for it to come back (tock). To compare the frequency of the two pendulums, we have \begin{align*} \frac{f_A}{f_B}&=\frac{\sqrt{\ell_B}}{\sqrt{\ell_A}}\\\\&=\frac{\sqrt{6}}{\sqrt{2}}\\\\&=\sqrt{3}\end{align*} Therefore, the frequency of pendulum $A$ is $\sqrt{3}$ times the frequency of pendulum $B$. A simple pendulum completes 40 oscillations in one minute. /Type/Font >> 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. Pennies are used to regulate the clock mechanism (pre-decimal pennies with the head of EdwardVII). Free vibrations ; Damped vibrations ; Forced vibrations ; Resonance ; Nonlinear models ; Driven models ; Pendulum . These NCERT Solutions provide you with the answers to the question from the textbook, important questions from previous year question papers and sample papers. 33 0 obj Thus, by increasing or decreasing the length of a pendulum, we can regulate the pendulum's time period. >> The period of the Great Clock's pendulum is probably 4seconds instead of the crazy decimal number we just calculated. 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 Resonance of sound wave problems and solutions, Simple harmonic motion problems and solutions, Electric current electric charge magnetic field magnetic force, Quantities of physics in the linear motion. /BaseFont/HMYHLY+CMSY10 Trading chart patters How to Trade the Double Bottom Chart Pattern Nixfx Capital Market. Problem (2): Find the length of a pendulum that has a period of 3 seconds then find its frequency. This method for determining If you need help, our customer service team is available 24/7. 11 0 obj endobj Some simple nonlinear problems in mechanics, for instance, the falling of a ball in fluid, the motion of a simple pendulum, 2D nonlinear water waves and so on, are used to introduce and examine the both methods. 500 500 611.1 500 277.8 833.3 750 833.3 416.7 666.7 666.7 777.8 777.8 444.4 444.4 708.3 795.8 767.4 826.4 767.4 826.4 0 0 767.4 619.8 590.3 590.3 885.4 885.4 295.1 /Name/F4 This book uses the The equation of period of the simple pendulum : T = period, g = acceleration due to gravity, l = length of cord. % 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 The displacement ss is directly proportional to . 42 0 obj /LastChar 196 /Type/Font endobj 656.3 625 625 937.5 937.5 312.5 343.8 562.5 562.5 562.5 562.5 562.5 849.5 500 574.1 /Name/F8 Problem (1): In a simple pendulum, how much the length of it must be changed to triple its period? WebSOLUTION: Scale reads VV= 385. /FontDescriptor 20 0 R /LastChar 196 In part a ii we assumed the pendulum would be used in a working clock one designed to match the cultural definitions of a second, minute, hour, and day. %
36 0 obj We move it to a high altitude. How to solve class 9 physics Problems with Solution from simple pendulum chapter? Here, the only forces acting on the bob are the force of gravity (i.e., the weight of the bob) and tension from the string. 20 0 obj Thus, The frequency of this pendulum is \[f=\frac{1}{T}=\frac{1}{3}\,{\rm Hz}\], Problem (3): Find the length of a pendulum that has a frequency of 0.5 Hz. sin Will it gain or lose time during this movement? Adding pennies to the pendulum of the Great Clock changes its effective length. . /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 You can vary friction and the strength of gravity. The two blocks have different capacity of absorption of heat energy. 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. 314.8 524.7 524.7 524.7 524.7 524.7 524.7 524.7 524.7 524.7 524.7 524.7 314.8 314.8 (Keep every digit your calculator gives you. Back to the original equation. << /Linearized 1 /L 141310 /H [ 964 190 ] /O 22 /E 111737 /N 6 /T 140933 >> /Name/F11 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? The only things that affect the period of a simple pendulum are its length and the acceleration due to gravity. 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 /Name/F6 <> Simple Harmonic Motion describes this oscillatory motion where the displacement, velocity and acceleration are sinusoidal. f = 1 T. 15.1. >> All Physics C Mechanics topics are covered in detail in these PDF files. x|TE?~fn6 @B&$& Xb"K`^@@ /BaseFont/WLBOPZ+CMSY10 Cut a piece of a string or dental floss so that it is about 1 m long. A simple pendulum is defined to have a point mass, also known as the pendulum bob, which is suspended from a string of length L with negligible mass (Figure 15.5.1 ). /BaseFont/OMHVCS+CMR8 endobj endobj 812.5 875 562.5 1018.5 1143.5 875 312.5 562.5] /Name/F1 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 >> Example Pendulum Problems: A. /Name/F3 i.e. g endobj 7 0 obj R ))jM7uM*%? (b) The period and frequency have an inverse relationship. Websimple harmonic motion. The answers we just computed are what they are supposed to be. Now use the slope to get the acceleration due to gravity. A pendulum is a massive bob attached to a string or cord and swings back and forth in a periodic motion. /Type/Font 795.8 795.8 649.3 295.1 531.3 295.1 531.3 295.1 295.1 531.3 590.3 472.2 590.3 472.2 /Widths[295.1 531.3 885.4 531.3 885.4 826.4 295.1 413.2 413.2 531.3 826.4 295.1 354.2 Set up a graph of period vs. length and fit the data to a square root curve. /Subtype/Type1 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. What is the period on Earth of a pendulum with a length of 2.4 m? 3.2. Consider the following example. I think it's 9.802m/s2, but that's not what the problem is about. /Subtype/Type1 We can solve T=2LgT=2Lg for gg, assuming only that the angle of deflection is less than 1515. For the next question you are given the angle at the centre, 98 degrees, and the arc length, 10cm. The individuals who are preparing for Physics GRE Subject, AP, SAT, ACTexams in physics can make the most of this collection. 639.7 565.6 517.7 444.4 405.9 437.5 496.5 469.4 353.9 576.2 583.3 602.5 494 437.5 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 To verify the hypothesis that static coefficients of friction are dependent on roughness of surfaces, and independent of the weight of the top object. Wanted: Determine the period (T) of the pendulum if the length of cord (l) is four times the initial length. In the case of a massless cord or string and a deflection angle (relative to vertical) up to $5^\circ$, we can find a simple formula for the period and frequency of a pendulum as below \[T=2\pi\sqrt{\frac{\ell}{g}}\quad,\quad f=\frac{1}{2\pi}\sqrt{\frac{g}{\ell}}\] where $\ell$ is the length of the pendulum and $g$ is the acceleration of gravity at that place. %PDF-1.2 Problems (4): The acceleration of gravity on the moon is $1.625\,{\rm m/s^2}$. 805.5 896.3 870.4 935.2 870.4 935.2 0 0 870.4 736.1 703.7 703.7 1055.5 1055.5 351.8 770.7 628.1 285.5 513.9 285.5 513.9 285.5 285.5 513.9 571 456.8 571 457.2 314 513.9 endobj
465 322.5 384 636.5 500 277.8 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 N*nL;5
3AwSc%_4AF.7jM3^)W? Exams will be effectively half of an AP exam - 17 multiple choice questions (scaled to 22. 18 0 obj The heart of the timekeeping mechanism is a 310kg, 4.4m long steel and zinc pendulum. endobj /Type/Font 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 If the length of the cord is increased by four times the initial length, then determine the period of the harmonic motion. PDF Notes These AP Physics notes are amazing! /Parent 3 0 R>> endobj /Subtype/Type1 Simple Pendulum: A simple pendulum device is represented as the point mass attached to a light inextensible string and suspended from a fixed support. WebSolution : The equation of period of the simple pendulum : T = period, g = acceleration due to gravity, l = length of cord. 24/7 Live Expert. /Name/F7 Current Index to Journals in Education - 1993 Webproblems and exercises for this chapter. The digital stopwatch was started at a time t 0 = 0 and then was used to measure ten swings of a /BaseFont/CNOXNS+CMR10 Here is a set of practice problems to accompany the Lagrange Multipliers section of the Applications of Partial Derivatives chapter of the notes for Paul Dawkins Calculus III course at Lamar University. The time taken for one complete oscillation is called the period. /FirstChar 33 8 0 obj We are asked to find gg given the period TT and the length LL of a pendulum. /Subtype/Type1 Given: Length of pendulum = l = 1 m, mass of bob = m = 10 g = 0.010 kg, amplitude = a = 2 cm = 0.02 m, g = 9.8m/s 2. How long is the pendulum? Use this number as the uncertainty in the period. 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 D[c(*QyRX61=9ndRd6/iW;k
%ZEe-u Z5tM A 2.2 m long simple pendulum oscillates with a period of 4.8 s on the surface of /LastChar 196 3 0 obj
680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 /FontDescriptor 14 0 R 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 Part 1 Small Angle Approximation 1 Make the small-angle approximation. 500 500 500 500 500 500 500 500 500 500 500 277.8 277.8 777.8 500 777.8 500 530.9 511.1 511.1 511.1 831.3 460 536.7 715.6 715.6 511.1 882.8 985 766.7 255.6 511.1] If you need help, our customer service team is available 24/7. What is the period of the Great Clock's pendulum? /LastChar 196 We can discern one half the smallest division so DVVV= ()05 01 005.. .= VV V= D ()385 005.. 4. >> How accurate is this measurement? 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. endobj A cycle is one complete oscillation. This leaves a net restoring force back toward the equilibrium position at =0=0. g 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.