PHYS 2326 HCCS useful equation

PHYS 2326 HCCS useful equation - PHYS 2325/2326 Useful...

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Unformatted text preview: PHYS 2325/2326 - Useful Formulae Introduction and Vectors Vectors zzz - zz zzz - zz V V V V z zzz - V - V zz z zzz zzz V V - V - V zz zzz zzz zzz . V V - {.V { V IJJ $ Dr. del Cerro - - $ IJ . . JJ # z V zz V zzz zz zz V - V W $ - { - { -{ - { $ Y - Y - . Ž‹ 7" Motion in One-Dimension For constant acceleration -I { $ I I  . =I Ž‹ I H7" . $ $ $ 7"  7" Ž‹  -  I{ . . - - { . I { . $ JI JJ 9 -I {{ -I { . { Motion in Two Dimensions Coordinate Systems J …‘• JJJ zX . zX z   z Y z Projectile Motion H . {–ƒ $ z Y z Y z IJ J $ - $ I  Ž‹ H7" z Y. . z z z - Y z …‘• J J$ {. IJ . $ …‘•$ - { •‹ { . $ zz X $ # JJ $ •‹ I . $ $ J J J I III Page 1 of 10 JI JJ J PHYS 2325 Useful Formulae Dr. C del Cerro z z z z Y Ž‹ z H7" z Y  - zz Y z Y Y - z - Y z z I zz X z z  - z { . . { I . $ IJ JJ I$ - I $ J I III JI JJ J I z | G| - z Relative Velocity J   J -   - z  z z X z X The Laws of Motion  I I More Applications of Newton’s Laws Motion with Resistive Forces zz .IY z W J $ I .I # I I For Horizontal Flat Curve J For Banked Curve IJ J JJ $ I $ $ . Ê $  F {. . # $ È { $ Energy and Energy Transfer For Constant Force z Ñ z J IJJ For Varying Force  {z{ z H  . # $ z zz VÑV Ñ Ñ Ñ Ñ z zz VÑV …‘• - Ñ Ñ - H .H For Spring  . . {. J  { $ . $ The Nonisolated System " # $ {. $ . {  $ H- - - - - The Isolated System $  H- JJ JJIJJJ J I Systems with Friction z X H- JJI J  z z Ñ z Dr. C del Cerro PHYS 2325 Useful Formulae Page 2 of 10 Work-Kinetic Energy Theorem H H .H $  $ . $ z Y     z ÑY . . H - H For Systems with Friction within System H -  . J J z Ñ z z Ñ Y z Potential Energy Conservative and Nonconservative Forces . H. . Potential Energy of a System z .  $ . z J # $ { { Ñ ? . C . . . J# J$ J z z z Y J IJ J z z z { Y{ J Momentum and Collisions Xzzz z  {z{ zX . zX   z z z  HJJ Conservation of Linear Momentum zzzzzzX - zzzz$zX z zzzzz - zzzzz # # $ zzzzzzzY - zzzzzzzY # $  zzzzzzzY - zzzzzzzY #  $ zzzzzzz - zzzzzzz # $ zzzzzzzz - zzzzzzzz #X $X zzzzzzXzY - zzzzzzXzz #z  $ zY zzzzzzXzY - zzzzzzzzz #z  $XY {z{ z  zH H Rotational Motion  Vector Product zz z z zz .V 0 V V0V 0 0 0 0 . 0 0 .0  0  . 0 J$ For constant acceleration . . { . $ $ - - { $ - . . { { . PHYS 2325 Useful Formulae Page 3 of 10 H Dr. C del Cerro Relationship between angular and tangential variables J I J $ I I$ 9J I$ J $ J I $ J & z  z JJ H H z H J $ JJ { •‹ {J   J -   H H Rolling Object, Centre of Mass J Angular Momentum z z 0 z z z I H H H H -H $ -H $ $ z#$ zz X . # $ J $ Newton’s Law of Universal Gravitation ## #$ Kepler’s Laws $ $ . 0 H J$ z Energy in Satellite Motion H $ . J . for elliptical orbit r=a $ z 0 z z H z 0 Y IJJJ IJ H IJJJ IJ H For circular orbit J %È$ J H For elliptical orbit I%È$ H I J I JJ I J H . 9 HJJ J HI Oscillatory Motion H $ …‘•$ { $$ •‹$ { -{ -{ PHYS 2325 Useful Formulae Page 4 of 10 Dr. C del Cerro {{ {{ I{ { I …‘•{ - { . •‹{ - { . $ …‘•{ - { $ JI JJ H- $ SHM Oscillator / { $ . H ${ / $ . $ For Simple Pendulum For Physical Pendulum H {{ J J { / { Energy in Waves in Strings JI J J { # { { J J{ $ {/ {{ J Mechanical Waves or •‹{ J{ { J . -{ •‹{ . . { { JJ J JJ $$ $$ I Displacement Wave Equation Pressure Wave Equation IJJ{ J Doppler Effect / { - $ IJJ{ { J J{ H H J J Superposition and Standing Waves . -{ Standing Wave { •‹ { …‘• For String Fixed at Both Ends J Beats # For Tube Open at Both Ends J J For Tube Closed at One End H J H …‘• # | . $| . $ F PHYS 2325 Useful Formulae Page 5 of 10 Dr. C del Cerro H 0 # # $ $ ' Fluid Mechanics $ ƒ ## - $$ - IJJJ . Temperature and Kinetic Theory of Gases { % { {{H H . { {H { { J J % ÈH %0 0 - H JH J JJ J J I $% $% H9 JI H H J JIJ I J $  $  %0 . $% H H JJ HJJJI J J I IJ J Root Mean Square Speed % % Average and Most Probable Speeds Energy in Thermal Processes: The First Law of Thermodynamics # I . /H . IJJJ IJ | & | PHYS 2325 Useful Formulae Page 6 of 10 Dr. C del Cerro Heat Engines, Entropy and the Second Law of Thermodynamics | |.| . | | | . | | | | J |J# ||J$ | J$ J X   Electric Forces and Electric Fields z#$ J# J$ J$ J #$ z  z z z zzzzX  J J J$ " %% 0 zz z V …‘• J #$ zz z V $ $ Electric Potential and Capacitance .J" J" . 9 Energy Stored in a Capacitor JJ JJ { {$ $ .  z zzzzJ For Point Charges  z zzzzJ J J J# J$ J#$ In a Uniform Electric Field: z . J For a Continuous Charge Distribution J J Parallel Plate Capacitor Combination of Capacitors JIJI # - $ - %# " Capacitance Capacitors with Dielectrics PHYS 2325 Useful Formulae Page 7 of 10 - $ - % - JJ J Dr. C del Cerro " " Current and Direct Current Circuits H H H JJ z Y . z J " {{ $ H Power Delivered to a Resistor H$ $ H "{ "{ -{. 0 -{. " {{ Equivalent Resistance # - $ - %# - $ - % - JIJI JJ J Kirchhoff’s Rules H Capacitor Charging J{ { H{ { J{ { . F Capacitor Discharging H{ { .H" Magnetic Forces and Magnetic Fields zzzzz z V JY 0 zz |J| •‹ J z τ  J z HV zzzzz H  0 z zzzzzzzz Hzzzz 0 z H z 0 zz V J PHYS 2325 Useful Formulae z 0 z H J zz z V Page 8 of 10 H Dr. C del Cerro H# H$ I æ. H{ { z † z æ . F $ " Faraday’s Law and Inductance 4 I IJ J 4 . z z H . æ H toroid JH JJ JJ . H{ { JI IJ J .H H HH$ $ æ H H z zz V z z V æ Electromagnetic Waves $ $ $ $ $ $ $ $ zz V z W H I z zz V z . "H æ - æ H I …‘•{ …‘•{ . . { { YX zz 0 V zz $ $ $ J •‹ I Reflection and Refraction of Light J$ F J# J# 2 J$ J# J J $J J $J J # # # J$ J J #J J #J J $ $ $ Wave Optics Spherical Mirror Equation J H J . J J Refraction by Spherical Surface J# J$ {J$ . J# { J J Thin Lens Equation {J . { # . $ F PHYS 2325 Useful Formulae Page 9 of 10 Dr. C del Cerro Wave Optics Double Slit Interference Constructive Interference { •‹ // Destructive Interference •‹ H // Thin Films Constructive Interference - F { { Destructive Interference J J -F { { { { { H …‘• $ {  GC ) Diffraction a) Single Slit { // I Limiting Angle of Resolution •‹ I b) Diffraction Grating •‹ { { { PHYS 2325 Useful Formulae Page 10 of 10 Dr. C del Cerro ...
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