Physics 12 Formula Sheet

Kinematics/Dynamics

average velocity 2

fi vv

t

dv

+== centripetal acceleration

2

22 4

T

r

r

vac

π==

linear acceleration t

vva

if −= centripetal force

2

22 4

T

rm

r

mvFc

π==

final velocity1 atvv if += speed on a curved bank

with neglible friction θtan⋅= rgv

linear displacement1 tvvd fi )(2

1+= Hooke’s law (elastic force) kxForxkF ee =−=

�

�

linear displacement2 2

2

1attvd i +=

period of a spring and mass

system k

mT π2=

final velocity2 advv if 222 += period of a pendulum g

lT π2=

velocity components θ

θ

sin

cos

iiy

ix

vv

vv

=

= torque Fr⊥=τ

Newton’s 2nd

law maFnet = Kepler’s third law 2

3

2

3

B

B

A

A

T

r

T

r=

gravitational force mgFg = Newton’s law of

universal gravitation 2r

GMmFg =

force components θ

θ

sin

cos

FF

FF

y

x

=

= gravitational field intensity

2r

GMg =

friction normf FF ⋅= µ orbital speed 32

T

GM

r

GMv

π==

uniform circular motion T

rv

π2=

Newton’s version of

Kepler’s third law 22

3

4π

GM

T

r=

Electricity and Magnetism

Coulomb’s law 2

r

kQqFQ =

electric potential

difference in uniform

electric field

EdV =

electric field intensity q

F

r

kQE

Q==

2 magnetic field intensity1 θsinor BILFILBF BB == ⊥

electric potential difference q

EV

Q∆= magnetic field intensity2 θsinor qvBFqvBF BB == ⊥

Momentum, Energy and Power

momentum mvp = kinetic energy 2

2

1mvEk =

impulse-momentum

theorem jtFvmp net ==∆=∆ gravitational potential energy mghEg =

work θcos⋅⋅= dFW elastic potential energy Ee =1

2kx

2

power t

EP =

Modern Physics

mass-energy equivalence 2mcE = deBroglie wavelength

mv

h=λ

energy of (a) photon(s) nhfE sphoton =)( energy of a hydrogen

atom orbital 2

6.13

n

eVEn

−=

speed of light with

universal wave equation λfc =

energy absorbed/ejected

photon ifphoton EEE −=

maxium kinetic energy

of a photoelectron WhfEk −=

max

dilated time and

proper time 2

2

0

1c

v

tt

−

∆=∆

stopping potential stopk qVE =max

contracted length and

proper length 2

2

0 1c

vLL −=

work function and

threshold frequency ohfW = relativistic mass and

rest mass 2

2

0

1c

v

mm

−

=

photon momentum λ

hp =

total, rest, and

kinetic energies kEcmmc += 2

0

2

a

acbbx

2

42 −±−=

c2 = a

2 + b2 − 2abcosC

C

c

B

b

A

a

sinsinsin==

acceleration due to gravity at Earth’s surface g = 9.81 m/s2 Element

atomic mass unit (amu) 1 u = 1.6605 × 10-27

kg 82 Lead (Pb)

charge of an electron e = 1.602 × 10-19

C 83 Bismuth (Bi)

Coulomb’s constant k = 9.0 × 109 N�m

2/C

2 84 Polonium (Po)

electron volt 1 eV = 1.602 × 10-19

J 85 Astatine (At)

gravitational constant G = 6.67 × 10-11

N�m2/kg

2 86 Radon (Rn)

mass of Earth 5.98 × 1024

kg 87 Francium (Fr)

mass of Sun 1.99 × 1030

kg 88 Radium (Ra)

radius of Earth 6.38 × 106 m 89 Actinium (Ac)

radius of Earth’s orbit 1.49 × 1011

m 90 Thorium (Th)

Planck’s constant h = 6.626 × 10-34

J/Hz 91 Protactinium (Pa)

rest mass of a neutron 1.008665 u = 1.675 × 10-27

kg 92 Uranium (U)

rest mass of a proton 1.007276 u = 1.673 * 10-27

kg 93 Neptunium (Np)

rest mass of an electron 9.109 * 10-31

kg 94 Plutonium (Pu)

speed of light in a vacuum c = 2.998 * 108 m/s 95 Americium (Am)