Blyth Academy SPH4U - Grade 12 University Physics

Physics Formula Sheet

CONSTANTS

gms

= 980 2. GN mkg

= ו−667 10 11

2

2. e C= × −160 10 19.

µ π074 10= ×

•− T mA

cms

= ×300 108.

m kge = × −911 10 31. m kgp = × −167 10 27. Planck’s Constant (h) 6.626 (10-34) Js Rest mass of electron (me) 9.11 (10-31) kg, 0.511 MeV/c² Mass of Earth (ME) 5.98 (1024) kg Radius of Earth (RE) 6.38 (106) m Mass of Sun 2 (1030) kg Earth – Sun distance 1.49 (107) km EQUATIONS Kinematics

vdt

v vav = =

+Δ

Δ1 2

2 a

v vtav =−2 1

Δ v v a t2 1= + Δ Δ Δ Δd v t a t= +1

212

Dynamics

F manet = F mgg = FGmmdg =1 22Δ

F Ff N= µ F kx=

avrc =2

F mamvrc c= =2

ar

Trfc = =

44

2

22 2π

π FF

mm

dd

1

2

1

2

2

1

2

=⎛

⎝⎜

⎞

⎠⎟

gGMR

= 2 vGMresc =

2

rT

GM3

2 24=

π v

GmrE2 =

Energy, Momentum & Power

W F d= Δ cosθ E mghGMmrg = = − E mvk =

12

2 E F dth f= Δ

E kxelastic =12

2 Tmk

= 2π PWtF dt

Fvav= = =Δ

Δ

Δ

kN mC

= ו

9 00 1092

2.

ΔΔ

dv v t

=+( )1 2

2Δ Δ Δd v t a t= −2

212

v v a d22

12 2= + Δ

Blyth Academy SPH4U - Grade 12 University Physics

p mv= p p= ' J F t m v p= = =Δ Δ Δ efficiencyWWoutput

input= × 100%

Electricity and Magnetism

Fkq qde =1 22Δ

ε =kqr 2

Ekq qrelectric =1 2

Vkqr

= ΔΔ

VWq

Eqe= = Δ

ΔV

Eq

de= = ±0

ε q Ne=

ε =ΔVr

(parallel plates only) − = −q V mv mvΔ 12 2

2 12 1

2

F qvB= sinθ F IlB= sinθ BIr

=µπ0

2 B

NIL=

µ0 Fl

I Id

o2 1 2

2=µ

π

Waves

fNt

=Δ

Tf

=1

vT

f= =λ

λ θ θi r=

sinsin

θθ

λλ

1

2

1

2

1

2

2

1= = =vv

nn

sin ( )( )θ λn dn= − 1

2

ΔxL d

=λ

xL

nnd= −( )( )1

2λ PS PS n1 2

12− = −( )λ

Matter-Energy Interface:

γ =

Time dilation: Δt = γΔto

Length contraction: L = γ−1Lo

Mass change: m = γmo

Relativistic Velocity ux' =

Rest energy: Eo = moc2

Total relativistic energy: E = mc2

Relativistic KE: KE = Eo (γ - 1)

Bohr atom: En =

De Broglie wavelength: λ =

Photon energy: E = h f

Photon momentum: p = =

Photoelectric effect: Ek = h f – W

Heisenberg’s Uncertainty Principle: ΔxΔp ≥ !

Radioctive decay: N = Noe-λ t N = No()

λ =

sinθ λm

md=

ncv

=

(1 − )− v² c²

(1 − ) uxv

c²

ux − v

-13.6 eV n²

h mv

t t

0.693 t

h λ

E c

Blyth Academy SPH4U - Grade 12 University Physics Important Mathematical Relationships for Physics

Trig Identities sin cos2 2 1θ θ+ = cos cos sin2 2 2θ θ θ= − sin sin cos2 2θ θ θ=

Quadratic Formula Quadratic Equation

ax bx c2 0+ + = xb b ac

a=− ± −2 4

2

sinθ = a/c cosθ = b/c tanθ = a/b Cosine Law: c2 = a2 + b2 - 2ab cos C

Sine Law: aA

bB

cCsin sin sin

= =

%erroractual measured

actualx=

−100%

a

b cA

BCc

θ

b

a