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summaries_hrw - Physics 317K Lecture Summaries Spring...

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Physics 317K Lecture Summaries Spring Semester 2001 Based in part on: Fundamentals of Physics , by Resnick, Halliday, and Walker, 6th Edition, Volume 1 (Wiley) Prepared by: S. Kopp, K. Lang and J. L. Ritchie Department of Physics University of Texas at Austin
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Contents 1 Math Mini Review 3 1.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Trigonometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2 Measurement (Chapter 1) 6 3 Motion Along a Straight Line (Chapter 2) 7 4 Vectors (Chapter 3) 9 5 Motion in Two and Three Dimensions (Chapter 4) 10 6 Force and Motion - I (Chapter 5) 11 7 Force and Motion - II (Chapter 6) 13 8 Kinetic Energy and Work (Chapter 7) 14 9 Potential Energy and Conservation of Energy (Chapter 8) 15 10 Systems of Particles (Chapter 9) 16 11 Collisions (Chapter 10 ) 17 12 Rotation (Chapters 11 ) 18 13 Rolling, Torque, and Angular Momentum (Chapters 12 ) 19 14 Equilibrium and Elasticity (Chapter 13) 20 15 Gravitation (Chapter 14 ) 21 16 Fluids (Chapter 15 ) 22 17 Oscillations (Chapter 16 ) 23 18 Waves I (Chapter 17 ) 24 19 Waves II (Chapter 18 ) 25 20 Temperature, Heat, and the 1 st Law of Thermodynamics (Chapter 19 ) 26 21 The Kinetic Theory of Gases (Chapter 20 ) 27 22 Entropy and the 2 nd Law of Thermodynamics (Chapter 21 ) 28 2
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1 Math Mini Review 1.1 Geometry Here are some areas of standard geometric figures that you should remember: 1. Triangle A = 1 2 base × height 2. Rectangle A = base × height 3. Circle A = π × radius 2 Triangle Rectangle Circle base base diameter height height radius The volume of a sphere is 4 3 πR 3 , its surface area is 4 πR 2 . The circumference of a circle is 2 πR , where R is the radius, or πD , where D is the diameter ( D = 2 R ). The volume of a right figure is is V = A × h , where h is the height of the figure, and A is the area of the base. If the base is a circle, then we’re talking about a right cylinder and A = πR 2 . If the base is a rectangle, you get the idea. Area height 1.2 Algebra Solving linear equations is easy: Ax + B = C implies the solution for x is x = ( C - B ) /A . Solving quadratic equations: Ax 2 + Bx + C = 0 implies x = - B ± B 2 - 4 AC 2 A . Solving a system of 2 equations with 2 unknowns: if A 1 x + B 1 y = C 1 A 2 x + B 2 y = C 2 (where the A i ’s, etc., are constants) then you can “solve” the first equation for x like x = ( C 1 - B 1 y ) /A 1 and insert this expression into the second equation. Then you will have a solution for y . Once you know y , you can use this value for y to solve for x . 3
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1.3 Trigonometry In the figure, the trigonometric functions sine, cosine, and tangent acting on the angle θ are defined as follows 1. tan θ = a/b 2. sin θ = a/c 3. cos θ = b/c 4. sec θ 1 / cos θ = c/b 5. csc θ 1 / sin θ = c/a 6. cot θ 1 / tan θ = b/a b a c θ A consequence of Pythagoras’ theorem is that sin 2 θ + cos 2 θ = 1 These are some useful values of the trig functions you should remember I reminded you of, but I will generally put these on exams for you: 1. sin 30 = 1 / 2, cos 30 = 3 / 2, tan 30 = 1 / 3, 2. sin 45 = 1 / 2, cos 45 = 1 / 2, tan 45 = 1, 3. sin 60 = 3 / 2, cos 60 = 1 / 2, tan 60 = 3, 4. sin 0 = 0, cos 0 = 1, tan 0 = 0, 5. sin 90 = 1, cos 90 = 0, tan90 = infinite , Radian vs.
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