Blyth Academy SPH4U - Grade 12 University Physics Physics Formula Sheet CONSTANTS g m s = 9 80 2 . G N m kg = × • − 6 67 10 11 2 2 . e C = × − 160 10 19 . μ π 0 7 4 10 = × • − T m A c m s = × 3 00 10 8 . m kg e = × − 9 11 10 31 . m kg p = × − 167 10 27 . Planck’s Constant (h) 6.626 (10 -34 ) Js Rest mass of electron (m e ) 9.11 (10 -31 ) kg, 0.511 MeV/c² Mass of Earth (M E ) 5.98 (10 24 ) kg Radius of Earth (R E ) 6.38 (10 6 ) m Mass of Sun 2 (10 30 ) kg Earth – Sun distance 1.49 (10 7 ) km EQUATIONS Kinematics v d t v v av = = + Δ Δ 1 2 2 a v v t av = − 2 1 Δ v v at 2 1 = + Δ Δ Δ Δ d v t at = + 1 2 1 2 Dynamics F ma net = F mg g = F Gm m d g = 1 2 2 Δ F F f N = μ F kx = a v r c = 2 F ma mv r c c = = 2 a r T rf c = = 4 4 2 2 2 2 π π F F m m d d 1 2 1 2 2 1 2 = g GM R = 2 v GM r esc = 2 r T GM 3 2 2 4 = π v Gm r E 2 = Energy, Momentum & Power W Fd = Δ cosθ E mgh GMm r g = = − E mv k = 1 2 2 E F d th f = Δ E kx elastic = 1 2 2 T m k = 2π P W t Fd t Fv av = = = Δ Δ Δ k N m C = × • 9 00 10 9 2 2 . Δ Δ d v v t = + ( ) 1 2 2 Δ Δ Δ d v t at = − 2 2 1 2 v v ad 2 2 1 2 2 = + Δ
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Physics Formula Sheet · · 2014-07-03Blyth Academy SPH4U - Grade 12 University Physics Physics Formula Sheet CONSTANTS g m s = 9.80 2 G N m kg = × 667 10−11 • 2. 2 e= 1.60×10−19C
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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