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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.

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MECHANICS (Kinematics and Dynamics)

av

rv

t

x

dxv

dt

avg

v v ua

t t

dva

dt

Average velocity

Instantaneous velocity in X direction

Average acceleration

Instantaneous acceleration in X direction

F m a

Fa

m

F m g

2

C

vF m

r

2

c

C

F va

m r

Newton’s Second Law

acceleration

Weight of an object

Centripetal force: uniform circular motion

Centripetal acceleration

AB BA

F F Newton’s Third Law

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rocket gasesF F

eg rocket propulsion

p mv

impulse J F t

J F t mv mu

0 0F 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

4

W F s

212K

E K mv

2 21 12 2

W F s mv mu

W qV

212K

E K mv 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 accelerating voltage

5

0

212

2 22

2

2

av

av

v u a t u v

s u t a t

v u a s

u vv

u vs v t t

Equation for uniform accelerated motion in one-dimension a = constant

2 2

212

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 vy t

2 2 2

2 2 2

tan

tan

y

x y s

x

y

x y v

x

ss s s

s

vv v v

v

Equations for

Projectile Motion

g = 9.8 m.s-2

ay = - g = - 9.8 m.s-1

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1 2

2

G m mF

r

planet

planet

planet

G Mg

R

1 2

p

m mE U G

r

pE U m g h

22

E E

E

G M G Mg

r R h

2L

Tg

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)

Period of pendulum g

7

3

2 24

r G M

T

3 3

1 2

2 2

1 2

r r

T T

32

3 3

1 2

2 2

1 2

22 1

1

r r

T T

rT T

r

orb

G Mv

r

2

orb

rT

v

2esc

G Mv

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

cv

c

0

02

21

tt t

v

c

2

0

0 21

LvL L

c

2E mc

2

21

mvp mv

v

c

2 2 2 2 4 2 2 2

0E p c m c p c E

22

02

21

mcK E E mc

v

c

212

K mv

00

EE 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

VR

I

P V I

Energy V I t

Resistance

Electrical power

Electrical energy

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MAGNETISM

1 2I IF

kL d

sinF B I L

0

2

IB

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

cosB

B A

B

t

Bd

dt

cos

sin

BB A t t

B A t

battery backI R

Magnetic flux

average induced emf

induced emf

electric motor: back

emf back

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p p

s s

V n

V n

ps

s p s p

p s

nnV V I I

n n

s p s s p pP P V I V I

2

lossP I R

Transformer equation: step up or step down voltages

ideal transformer

Power loss (eddy currents – transformer, induction heating; transmission lines)

sinF qv B

FE

q

VE

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

212mv eV

212

21max min2

21max min2

h f m v W

h f m v W

m v h f W

21max2

min

s

s

eV mv

Wh fV

e e

21max2

min

min

0s

c c

eV mv

Wh 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

sinn d

2 2

1 1 1

f i

Rn n

2 1E E h f

2

hL mv r

1

1213.6 eV

n

EE E

n

2 11

1 15.29 10 m

nr 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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h

mv

hE h f c f p

h hp

p

4

hx p

de Broglie wavelength de Broglie relationship

Photon

Matter wave

Heisenberg Uncertainty Principle

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The NUCLUES

products reactantsm M M

2E mc

9 4 12

4 2 6

1

0Be He C n

Beta minus decay

en p e

232 228 4

90 88 2

4

2

Th Ra He

He

Mass defect

Einstein – mass/energy

Chadwick discovers neutron

Beta decay Pauli & Fermi neutrino

Alpha decay

Beta plus decayp+ n + e+ + e

19Ne10 19F9 + e+ + e

e+ +

p[d(-1/3) u(+2/3) u(+2/3)] n[d(-1/3) u(+2/3) d(-1/3)]

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Standard model

Proton

Neutron

Nuclear fission

protond (-1/2)u (+2/3)u (+2/3)

neutrond (-1/3)u (+2/3)d (-2/3)

235U92 + 1n0

236U92* 136Xe56 + 88Sr36 + 121n0