This formula sheet shows all of the formula given on the VCAA exam. It is assumed that students know the context that each formula would be used in; the focus of this sheet is to show all of the re-arrangements that could be required / used.Formulae marked with * are not included on the VCAA sheet, but are derived from included formulae and may still be of use in some of the questions.

Kinematics

v =u+at u =v −at , t =

v −ua

, a=

v −ut

s=ut+

12

at2

t=

2sa

(if u=0)

v2 =u2+2as v = u2+2as , u= 2as−v 2 ,

s=

v 2−u2

2a, a=

v 2−u2

2s

s=

12

(u+v )t t=

2s(u+v )

s=vt−

12

at2

t=

2sa

(if v=0)

Circular motion

a=

v 2

r v = ar , r =

v 2

a

a=

4π 2rT 2

T =

4π 2ra

, r =

aT 2

4π 2

VCE Physics.com - Physics 3&4 exam formula sheet 2017

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Projectile motion

Vvertical =Vsinθ *

Vhorizontal =Vcosθ *

t =

2v sinθg

*

(These equations are based on starting and finishing at the same height)

H =v 2 sin2θ

2g* (These equations are based on starting and finishing at the

same height)

R =

v 2 sin2θg

*

(These equations are based on starting and finishing at the same height)

h(x )= tanθx −

g2v 2 cos2θ

x 2 *

Forces & energy

F∑ =ma a=

Fm

F =−kΔx k =

Fx

, x =

Fk

(- just indicates opposite direction)

E =

12

k(Δx )2

Δx =

2Ek

, k =

2E(Δx )2

E =mgΔh h =

Emg

, g =

Emh

, m =

Egh

E =

12

mv 2

v =

2Em

, m =

2Ev 2

p =mv v =

pm

Δp =FΔt F =

ΔpΔt

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Gravitational fields

F =

GM1M2

r 2 r =

GM1M2

F

g =

GMr 2

r =

GMg

r 3

T 2 =GM4π 2

r =

GMT 2

4π 23 ,

T =

4π 2r 3

GM, M =

4π 2r 3

GT 2

v 2

r=

GMr 2

v =

GMr

, r =

GMv 2

Fields & applications of field concepts

E =

Vd V =Ed

12

mv 2 =qV v =

2qVm

E =

kqr 2

r =

kqE

F =qE E =

Fq

F =

kq1q2

r 2

F =qvB q =

FvB

, v =

FqB

, B=

Fqv

F = ILB I =

FLB

, B =

FIL

, L=

FBI

r =

mvqB

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Generation and transmission of electricity

R = r1+r2+ .....

1R=

1r1

+1r2

+ ..... R =

r1r2

r1+r2

, r2 =

Rr1

R −r1

V = IR R =

VI

, I =

VR

P = IV P =

v 2

R, P = I 2R (combined with equations above)

V1

V2

=N1

N2 V1=V2

N1

N1

, V2 =V1

N2

N1

, N1=N2

V1

V2

, N2 =N1

V2

V1

I2

I1

=N1

N2

V1=V

r1

r1+r2

⎛

⎝⎜⎞

⎠⎟*

V2 =V

r2

r1+r2

⎛

⎝⎜⎞

⎠⎟

Vrms =

12

Vpeak Vpeak = 2×Vrms

F = ILB I =

FLB

, B =

FIL

, L=

FBI

ε =−N

ΔφΔt

φ =BA

Einstein’s special relativity

γ =1

1−v 2

c2 t =t0γ , m =m0γ ,

L=

L0

γ

E rest =mc2

c =

Em

Etotal =γmc2

Ekinetic =(1−γ )mc2

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The nature of light and matter

Emax =hf −W W =Emax −hf , f(threshold ) =

Wh

(If electrons have 0 energy)

E =hf f =

Eh

, h =

Ef

p =

hλ

λ =hp

E =

hcλ

* λ =

hcE

Δp xΔx ≥

h4π

Wave concepts

v =fλ f =

vλ

, λ =

vf

Path difference = nλ(constructive interference)

Path difference =

n−12

⎛⎝⎜

⎞⎠⎟λ (destructive interference)

Δx =

λLd

n1sinθ1=n2sinθ2

θ2 =sin−1 n1

n2

sinθ1

⎛

⎝⎜

⎞

⎠⎟

n1v 1=n2v 2

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Data

Acceleration due to gravity g=9.8m /s2

Rest mass of electron me =9.1×10−31kg

Electron charge e=1.6×10−19C

Planck’s constant h=6.63×10−34 Js

Speed of light in vacuum c =3.0×108 m /s

Gravitational constant G =6.67×10−11Nm2 /kg2

Mass of earth m=5.98×1024 kg

Radius of Earth RE =6.37×106 m

Coulomb’s constant k =8.99×109Nm2 /kg2

Prefixes / Units

p = pico = 10−12n = nano = 10−9

μ = micro = 10−6m = milli = 10−3

k = kilo = 103M = mega = 106

G = giga = 109 t = tonne = 103kg

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