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Math Review for Physicists Vocabulary: accuracy, precision, linear, exponential, inverse, root curve, dimensions, independent variable, dependent variable Triangles:  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , Pythagorean theorem: a2 + b2 = c2 Significant Figures Sig figs with addition/subtraction (fewest decimal places) Sig figs with multiplication/division (fewest sig figs in any of the factors) Units/Unit Conversion Standard SI units (kg, m, s, C, etc.) Conversions (giga, mega, kilo, hecta, deka, deci, centi, milli, micro, nano, pico) Dimensional consistency (check to see if the units in an equation work) Linear Relationships Slopes/intercepts Meaning of the slope Writing equation from a linear graph Using the equation to answer questions about the data Graph Shapes (recognize shapes) Linear: y = kx + b Exponential: y = kxn + b Inverse: y = kx-n + b Root Experimental Conditions Independent and dependent variables Recognize which variables are held constant II. Mechanics Section 1: Position, Velocity and Acceleration Vocabulary: vector, scalar, position, distance, displacement, speed, velocity, strobe diagram, motion map, frame of reference, average velocity, instantaneous velocity, average acceleration, instantaneous acceleration Strobe diagrams and motion maps How to draw and interpret them Frame of reference x vs. t, v vs. t, a vs. t graphs finding equation that describes a linear graph converting among graphs converting between graphs and verbal descriptions converting between graphs and strobe diagrams/motion maps slope of x vs. t curve = instantaneous velocity slope of v vs. t curve = instantaneous acceleration area under v vs. t curve = Dx area under a vs. t curve = Dv Comparing motion of two objects graphically  EMBED Equation.3 ,  EMBED Equation.3  Vectors (displacement, velocity, acceleration, force, momentum) and scalars (distance, speed) III. Mechanics Section 2 One Dimensional Kinematics (constant acceleration) Vocabulary: freefall, kinematics Stacks of kinematics curves Equations  EMBED Equation.3   EMBED Equation.3   EMBED Equation.3  g = 9.8 m/s2 downward (any object in the air on earth has an acceleration of g!) Describe x, v, and a for an object tossed straight up into the air Goal 2: Two Dimensional Kinematics (motion in two dimensions!) IV. Mechanics Section 4 Projectile Motion Vocabulary: projectile, trajectory, horizontal component, vertical component, range, hang time/flight time, frame of reference, air resistance, apogee, perigee Projectile: any object on which gravity is the only force Acceleration of a projectile (on Earth) is always g (9.8 m/s2) Divide problem into horizontal and vertical parts Horizontal Horizontal component of velocity is always constant (a = 0)  EMBED Equation.3  Vertical Vertical acceleration is always = g All equations from last unit apply, and acceleration = g:  EMBED Equation.3  and  EMBED Equation.3  Any given quantity that is neither horizontal nor vertical must be resolved into its components For a projectile launched horizontally, flight time depends only on the height from which it was launched For projectiles launched at angles: REMEMBER TO RESOLVE THE INITIAL VELOCITY INTO COMPONENTS!! Effect of air resistance on trajectory Satellite Motion V. Mechanics Section 5 Circular Motion Vocabulary: uniform circular motion, circumference, tangential/linear velocity, centripetal acceleration, centripetal force, centrifugal force Centripetal vs. centrifugal force and Newtons 1st Law  EMBED Equation.3 , where T is the period  EMBED Equation.3 ,  EMBED Equation.3  Centripetal force is a net force! Identify centripetal forces on different objects (gravity, tension, friction (unbanked curve), friction & normal force (banked curve), etc) Remember  EMBED Equation.3  Newtons Law of Universal Gravitation:  EMBED Equation.3  Goal 3 and 4: Forces VI. Mechanics Section 3 Forces Vocabulary: Force, inertia, agent, object, net force, terminal velocity, equilibrium, contact force, field force, force of gravity, normal force, force of static friction, force of kinetic friction Newtons Laws of Motion Inertia Fnet = ma Equal and opposite force pairs (agent/object notation) Types of forces Applied, tension, kinetic friction, static friction, air resistance, normal, buoyant Gravitational, electric, magnetic Free-body diagrams Draw them Calculate individual forces Calculate net force Objects on flat ground or on an incline Equilibrium Forces Find unknown force when Fnet = 0 Find force that will make Fnet = 0 Force of friction Kinetic and static friction Ff = mFN Torque Torque = perpendicular force x lever arm Formula: t = F4%"d Goal 6: Momentum and Impulse VII. Mechanics Section 6  Momentum and Impulse Vocabulary: inertia, momentum, elastic, inelastic, impulse Remember: Inertia Momentum Takes into account both inertia (mass) and velocity p = mv Momentum is a vector Units: kg"m/s Conservation of Momentum Total momentum is always conserved (The most unbreakable law in the universe!) For the system as a whole: pinitial = pfinal To solve momentum problems: Define an initial state and a final state Write an equation for the initial momentum Write an equation for the final momentum Set them equal and solve pinitial = pfinal Elastic (bouncing) and Inelastic (sticking) Collisions Impulse Impulse is a change in momentum. FnetDt = mDv = Dp For impulse calculations where the force is changing, use the average force Practical applications (bat and ball, car airbags, gymnastics mats, safety nets, car crashes, jackhammer) Goal 5 and 8  Work, Energy, and Thermodynamics Vocabulary: Energy, work, power, kinetic, gravitational potential, elastic potential, spring constant, internal energy, conservative force, heat, thermal equilibrium, specific heat, entropy Energy the ability of an object to produce change in itself or its environment unit Joule (J) = N(m Ways to represent energy Energy pie charts Energy flow diagrams Energy bar graphs Forms of Energy Storage Kinetic Energy Is the object moving? KE = mv2 KE is a scalar (technically depends on speed, not velocity) Soup can lab: translational and rotational KE KE is conserved in elastic collisions, but not in inelastic collisions Gravitational Potential Energy Is the object some distance above the ground (or other reference point)? GPE = mgh Must pick a reference point Elastic Potential Energy Is there a spring or other elastic object that is either stretched or compressed? EPE = kx2 x is the displacement from rest (non-stretched or compressed) position DEPE = EPEf - EPEi F = kx (Hooke s Law  force needed to stretch/compress a spring) Chemical Energy  Energy stored in chemical bonds Internal (Thermal) Energy  Is there friction or some type of collision/compression? Methods of Energy Transfer Working  It s working if there is a change in energy and it s not either of the other two! Heating  Change in temperature Radiating  emitting electromagnetic waves Work is a change in energy (W = DE) W = DE = FDx W is + if energy is put into the system W is  if energy is removed from the system Power The rate at which energy is transferred Unit  Watt (W) = J/s  EMBED Equation.3  Conservative and Non-conservative forces Conservative  energy transfer is reversible; DE depends only on the initial and final positions. 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Friction) Heating Temperature  the average kinetic energy of the molecules in a substance Conduction (materials in contact) and convection (motion of a fluid) Specific heat Q = mcDT Achieving Thermal Equilibium (two substances of different temperatures in contact) Qlost = Qgained  m1c1DT1 = m2c2DT2 Calorimeter Change in internal energy = working + heating DU = Q + W Remember to use the correct signs! 1st Law of Thermodynamics Conservation of energy 2nd Law of Thermodynamics Thermal Energy flows spontaneously from a hot object to a cooler one One cannot convert thermal energy completely into useful work (eff = 1 work/fuel) Every isolated system becomes more disordered as time passes (Entropy) Goals 9 and 10: Electricity and Magnetism Vocabulary: insulator, conductor, semiconductor, conduction, induction, electric potential difference, series, parallel, paramagnetic, diamagnetic, ferromagnetic, motor, generator Electrostatics Electric Charge and Charge Transfer Properties of charge (likes/unlikes, conserved, quantized) Insulators/Conductors/Semiconductors Milliken Oil Drop Experiment (showed charge is quantized) Charging by conduction/induction Induced charge separation (conductor)/polarization (insulator) Coulombs Law F = kq1q2/r2 Electric force is a field force, generally stronger than gravity Apply to two charges or multiple charges Electric Field Lines away from +, toward closer lines ( stronger field direction of field at a point is the tangent to the field line at that point Electric Potential Difference Volt = J/C V = W/q V = Ed Electric Current I = DQ/Dt (Ampere = C/s) Conditions for Current Flow Electric potential difference Closed path DC Circuits Schematic Circuit Symbols Ohms Law: V = IR Series Circuits: I is same everywhere VT = V1 + V2 + V3 + RT = R1 + R2 + R3 + Parallel Circuits: IT = I1 + I2 + I3 + V is same everywhere 1/RT = 1/R1 + 1/R2 + 1/R3 + Complex Circuits simplify Power P = IV = I2R (unit: Watt) Energy dissipated by a circuit element: E = PBC        1 2 3 7 8 < =   Z [ 6 7 ˽殠摃{r{r{riieeh=h=CJH*aJh=CJH*aJh=CJaJj'h=CJEHUaJjH h=CJUVaJjh=CJEHUaJjH h=CJUVaJjh=CJEHUaJj[H h=CJUVaJjh=CJUaJh=CJaJh=CJ aJh=5CJaJ'#BC> R  j  K k ~   & Fd  & Fd h^h$a$ww  Z [ 6 7 W v F)Z +,h^h & Fd & Fd  & Fd 7 ,.8:)*=>?@BCVWXY +,RSfȺh=CJ aJh=5CJaJh=5CJ aJjh=CJEHUaJj+agG h=CJUVaJj:h=CJEHUaJj,agG h=CJUVaJjh=CJUaJh=CJOJQJaJh=6CJaJh=CJaJ/,HRj/01qrAB}5MV & F 8d x^` & Fd x & Fd x$a$ & Fd  & Fd fghijk~.01qο΢΋΂΋΋΋zqfqz[h=6CJ]aJh=5>*CJaJh=5CJaJh=CJaJh=CJH*aJh=6CJaJjh=CJEHUaJjUgG h=CJUVaJjf h=CJEHUaJj,gG h=CJUVaJh=CJaJjh=CJUaJj h=CJEHUaJj#gG h=CJUVaJ ./56IJKLMwx8:?@STŷਚ}tpgXjglG h=CJUVaJh=CJH*aJh=h=5CJaJj h=CJEHUaJj|lG h=CJUVaJjh=CJEHUaJj|lG h=CJUVaJj|h=CJEHUaJj{lG h=CJUVaJjh=CJUaJh=CJaJh=6CJ]aJh=6CJH*]aJ VzJ;LMwx?nMn$a$ & Fx & Fd x & Fd xvd x^`v & F  d x^`TUV^_noVWjklmõݦ݉{l^Uh=5CJaJj!h=CJEHUaJjlG h=CJUVaJjh=CJEHUaJj6lG h=CJUVaJjh=CJEHUaJjlG h=CJUVaJj^h=CJEHUaJjlG h=CJUVaJh=6CJ]aJh=CJaJjh=CJUaJj@h=CJEHUaJ8;[^PRz|.06TVt """""""""####ۭϭ䩖 h=CJh=5>*CJ\h=>*CJaJh=h=6CJaJh=6CJOJQJaJh=CJOJQJaJh=CJOJQJaJh=CJH*aJh=CJaJh=5CJaJh=5>*CJaJ7 u @cuh & Fd x & Fd xh^h.0JXp , W !""" & Fd x & Fd xh^h$a$"#####$$$ %!%:%L%a%s%%%%%'&n&&  & F !d  & F !d  & F !d  !d$da$d & Fd x##$$$$%%%%%:&A&Y&b&t'u'v'w'x'(((("($(0(2(:+B+N+n+z+|+++++,,,,,,--~..D0F0111111 1(1*1,1.10121j#h=CJEHUjA%H h=CJUVaJjh=CJU h=CJH*h=CJOJQJ h=CJH*h=6CJ] jh=CJ h=>*CJ h=CJ h=CJ>&&&k'w''&(( )))**:++++D,P,,,,N-../  & F !d  & F !d  & F !d//080J00161N111262P22203Z3[3344)4M4 & F  & F ^$a$  & F !d  & F !d214111227292/303Z3[5\5]5^5`5a56 6^7`7d7f7p8q8u8v8z8{888888888888888888888888888+9,9:bbFfHfgg`hbhhhhhh=CJOJQJh=6CJ]U jh=CJh=6>*CJOJQJ^Jh= h=CJH*h=CJOJQJ h=CJ h=CJH*EM44445G5U5b55555*6677&747V7777 8818D8l88^ & F  & F  & F 888889!9;9b8bLbb ccccFdfddeefn1), bends toward normal wave speeds up (n2<n1), bends away from normal Snell s Law: n1sinq1 = n2sinq2 dispersion (prism, rainbow) Total Internal Reflection Only when going from higher to lower n Critical angle: qc = n1/n2 where n1>n2 Diffraction Light Electromagnetic Spectrum Speed of Light Optics Ray diagrams Real/virtual, enlarged/reduced/neither, upright/inverted M = di/do = Si/So 1/f = 1/di + 1/do     ghiiliiHjjjjkBkk*CJDpqqq4rrr s6sHssst2ttt(u`uuu2vJvVvvvvv@wdww & F  & F  & F uu"u$u&uuuuvvvvvvvvv&v(v*v,v.v0v2vJvJwLwPwRwZw\w`wbwvwxwwwwwwwwwwwwwwﻷjh=U h=>*CJh= h=CJH*h=6CJH*h=6CJ] h=6CJ h=CJ]h=6CJOJQJ] h=CJh=6CJH*]/wwwwwwwwwwww ,1h/ =!"# $ % / 01h/ =!"#$% ,1h/ =!"#$% Dd ,J  C A? 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