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 - .  7" Motion in One-Dimension For constant acceleration -I { \$ I I  . =I  I H7" . \$ \$ \$ 7"  7"   -  I{ . . - - { . I { . \$ JI JJ 9 -I {{ -I { . { Motion in Two Dimensions Coordinate Systems J  JJJ zX . zX z   z Y z Projectile Motion H . { \$ z Y z Y z IJ J \$ - \$ I   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  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{ zX . zX   z z z  HJJ Conservation of Linear Momentum zzzzzzX - zzzz\$zX z zzzzz - zzzzz # # \$ zzzzzzzY - zzzzzzzY # \$  zzzzzzzY - zzzzzzzY #  \$ zzzzzzz - zzzzzzz # \$ zzzzzzzz - zzzzzzzz #X \$X zzzzzzXzY - zzzzzzXzz #z  \$ zY zzzzzzXzY - zzzzzzzzz #z  \$XY {z{ z  zH 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 \$  ## - \$\$ - 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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