VISUAL PHYSICS ONLINE EQUATION MINDMAPS

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VISUAL PHYSICS ONLINE

EQUATION MINDMAPS

Equations are essential part of physics, without them, we can’t start to explain our physical world and make predictions. An equation tells a story – a collection of a few symbols contains a wealth of information. Many examination questions can be answered by having an in-depth understanding of equations. To help you maximize your examination marks, you should use the equation mindmaps to gain this in-depth understanding. You need to commit to memory much of the information contained in the equation mindmaps so that you can appreciate the story told by each equation.

• State what the symbols represent (meaning & interpretation), S.I. units, other units, typical values, vector or scalar, positive or negative quantity.

• A visualisation of what the equation is about, is it a definition or a law, when is it applicable, comments and an interpretation. • Alternative forms of the equation.

• Graphical representations of the equation. • Numerical examples.

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MECHANICS (Kinematics and Dynamics)

av r v t    x dx v dt  avg v v u a t t      dv a dt  Average velocity Instantaneous velocity in X direction Average acceleration Instantaneous acceleration in X direction F  m a



F a m 



F m g 2 C v F m r  2 c C F v a m r  

Newton’s Second Law

acceleration

Weight of an object

Centripetal force: uniform circular motion

Centripetal acceleration

AB BA

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3 rocket gases F  F eg rocket propulsion p  m v impulse J  F t J   F t mvmu 0 0 F    p



Momentum of a moving object

Impulse of a force F acting for a time interval t

Impulse = change in momentum

Law of Conservation of momentum

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4 W  F s 2 1 2 K E  K  m v 2 2 1 1 2 2 W   F s m v  mu W  qV 2 1 2 K E  K  m v e V

Work done by a force during a displacement (force and displacement in same direction [1D] Kinetic energy of a moving object

Work done = change in KE [1D] only

Work done on a charge in an electric field

Gain in KE electron due to a constant

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5 0 2 1 2 2 2 2 2 2 av av v u a t u v s u t a t v u a s u v v u v s v t t            

Equation for uniform

accelerated motion in one-dimension a = constant 2 2 2 1 2 0 cos sin 2 2 x x x x x y y y y y y y y y y y y a u u v u x u t a g u u v u a t v u a y y u t a t u v y t                       2 2 2 2 2 2 tan tan y x y s x y x y v x s s s s s v v v v v         Equations for Projectile Motion g = 9.8 m.s-2 ay = - g = - 9.8 m.s-1

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6 1 2 2 G m m F r  planet planet planet G M g R  1 2 p m m E U G r    p E U m g h





2 2 E E E G M G M g r _R _h    2 L T g   Gravitational force

Acceleration due to gravity at surface of a planet

Gravitational potential energy

Gravitational potential energy near Earth’s surface Acceleration due to gravity (Earth)

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7 3 2 2 4 r G M T   3 3 1 2 2 2 1 2 r r T  T 3 2 3 3 1 2 2 2 1 2 2 2 1 1 r r T T r T T r         orb G M v r  2 orb r T v   2 esc G M v r 

Kepler’s Third Law for satellite motion orbital velocity orbital period geostationary satellite T = 24 hours escape velocity

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SPECIAL RELATIVITY

2 2 1 1 v c v c      0 0 2 2 1 t t t v c     2 0 0 1 2 L v L L c     2 E  m c 2 2 1 m v p m v v c     2 2 2 2 4 2 2 2 0 E  p c m c  p c  E 2 2 0 2 2 1 m c K E E m c v c      2 1 2 K  m v 0 0 E E E p c p c    mass m is a constant time dilation length contract total energy momentum total energy kinetic energy kinetic energy v << c photon

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ELECTRICITY

V R I P V I Energy V I t    Resistance Electrical power Electrical energy

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MAGNETISM

1 2 I I F k L  d sin F  B I L  0 2 I B r    cos F d n B I A     

Magnetic force between two parallel conductors

Magnetic force on a conductor

Magnetic field surrounding a long straight conductor Torque Torque on a coil in a magnetic field cos B B A    B t     B d dt    

 

cos sin B B A t t B A t           battery I R back    Magnetic flux

average induced emf

induced emf

electric motor: back emf _back

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11 p p s s V n V  n p s s p s p p s n n V V I I n n   s p s s p p P  P V I V I 2 loss P  I R Transformer equation: step up or step down voltages

ideal transformer

Power loss (eddy currents – transformer, induction heating; transmission lines) sin F  q v B  F E q  V E d 

Force on a charged particle moving in a magnetic field Electric field

Electric field (constant) between two parallel charged plates

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NATURE OF LIGHT

E h f c  f  Energy of a photon Speed of light Speed of electromagnetic radiation 2 1 2m v eV 2 1 2 2 1 max min 2 2 1 max min 2 h f m v W h f m v W m v h f W       2 1 max 2 min s s eV m v W h f V e e    2 1 max 2 min min 0 s c c eV m v W h f W f h    

Gain in KE of electron due to accelerating voltage

Photoelectric Effect

Stopping voltage

Cut-off (critical) frequency

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THE ATOM

sin n  d  2 2 1 1 1 f i R n n     __  __   2 1 E E  h f 2 h L m v r    1 1 2 13.6 eV n E E E n    2 11 1 1 5.29 10 m n r  r n r   

Bragg’s Law – crystal structure (constructive interference)

Hydrogen atom - spectrum

Energy levels

Bohr Model of atom

Angular momentum quantized

n = 1, 2, 3, …

Energy levels hydrogen atom

Allowed orbits for electrons in hydrogen atom

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15 h m v   h E h f c f  p     h h p p     4 h x p     de Broglie wavelength de Broglie relationship Photon Matter wave Heisenberg Uncertainty Principle

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The NUCLUES

products reactants m M M    2 E 



m c 9 4 12 4 2 6 1 0 Be  He  C  n

Beta minus decay

e n  p e   232 228 4 90 88 2 4 2 Th Ra He He

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   Mass defect Einstein – mass/energy Chadwick discovers neutron Beta decay Pauli & Fermi

neutrino

Alpha decay

Beta plus decay

p

+

 n + e

+

_{+ }

e 19_Ne 10  19F9 + e+ + e e+ + p[d(-1/3)u(+2/3)u(+2/3)]  n[d(-1/3)u(+2/3)d(-1/3)]

VISUAL PHYSICS ONLINE EQUATION MINDMAPS