Honors Physics Formula Sheet

Final Exam

Circular and Rotational Motion

Δθ = θf – θi

ωavr =

=

θ – θ

=

α = ω – ω

s=θr

vt = ωr

at = αr

θ = ωot + ½αt2

ωf = ωo + αt

ωf2 = ωo

2 + 2αθ

centripetal acceleration & force

ac =

=

Fc = m(ac)

tangential velocity and tangential acceleration

vt = ωr

at = αr

rotational Motion

vt = ω r at = α r

s = θr

torque

τ = rF

τ = Iα

moment of inertia

I = (coefficient) mr2

rotational kinetic energy

KE = ½ Iω2

rotational work

work = τθ

rotational power

Power = τω

angular momentum (L)

conservation of momentum

Lo = Lf Ioωo = Ifωf

Solids and Fluids

Area circumference

circle A = πr2 2 π r

sphere A =4 πr2

Volume

sphere vol =

πr

3

pressure

press =

liquid

press = ρgh

barometric pressure

press atm = ρgh = density of mercury

= 13.6 x103 kg/m

3

absolute pressure

pressabs = pressatm + gauge press

buoyant force

Fb = mfg = ρgV V = volume

Apparent weight

apt wgt = actual weight – Fb

Equation of continuity for fluid

A1v1 = A2v2 A = area v = velocity

Elasticity

Young’s Modulli modulus =

Y=

Y =

S =

S =

B = -

= - (press)

Vibrations and Oscillations

T=

f=

T = 2π√

f =

√

Hooke’s Law and Acceleration

F = -kx F = ma a = -kx

a = -

ax = - ω2 x

amax = - ω2A

ω2 =

ω =√

ω =

= 2πf

Total energy in elastic material (spring)

Et = ½ kA2 PE = ½ kx

2 KE = ½ mv

2

Et = PE + KE

½ kA2 = ½ kx

2 + ½ mv

2

Position of mass in SHM

x = A cos θ

x = A cos ωt

x = A cos

x = A cos 2πft

Velocity in SHM

Et = PE + KE

½ kA2 = ½ kx

2 + ½ mv

2

kA2 = kx

2 + mv

2

kA2- kx

2 = mv

2

k(A2 – x

2) =mv

2

v2 =

(A2

- x2)

vmax = √

√ = √

A = ωA

vx = -vmax sinθ

vx =- vmax sinωt

vx = -vmax sin

vx =-vmax sin2πft

vx = -ωAsinωt

Simple pendulum

T=2 π√

Waves

Velocity v = λf v= λ

=

Velocity of mechanical waves

Solid

v √

Liquid

√

String

v = √

u = linear density = mass/length

u = kg/meter

Intensity, I =

Area = area of sphere

= 4πr2

Sound

Velocity of sound in air

v = 331m/s + .6(T) T = __CO

Intensity

I = Power /Area area = 4πr2 (area of sphere)

Threshold of hearing Io = 1 x 10-12

w/m2

Decibels

dβ = 10 Log

Doppler Effect

Moving source fobserved = (

)

Moving observer fobserved = (

)

Faster than sound (Mach Speed)

M =

Sin θ=

=

Electric Charges, Forces and Fields

1 - coulomb (-C) = charge on 6.24 x 1018

electrons

1+coulomb (+C) = charge on 6.24 x 1018

protons

1 electron = -1.602 x 10-19

C

1 proton = +1.602 x 10-19

C

q = -ne e = elementary charge =1.602 x10-19

C

Coulomb’s Law

F= k

k = 8.99 x 10

9

electric Field (E)

E =

(between parallel plates)

E =

(between parallel plates)

=permittivity of free space =

=8.854 x10

-12

E =

= k

(point charge)

Gauss’s Law

= flux of the electric field

= A =E = EAcosθ

= 4 πkq = q/

Electric Potential, Capacitors, and Dielectrics

electric potential energy (PE)

PE = -Work (electric field)

PE = qEd uniform electric field

PE = k

point charge

electric potential (voltage)

V=

=

=

V =

point charge

V = Ed uniform electric field

potential difference

In Uniform Electric Field

∆V = E∆d

Point Charge

ΔV =

-

capacitors

capacitance (C)

C = Q/ΔV

C=

C=

εo = 8.85 x 10-12

Capacitance with dielectrics

C=

=

κ = dielectric constant

energy stored in a capacitor

PE= ½ QΔV = ½ CV2 = ½

Electric Currents and Circuits

electric current (I)

I =

1 amp =

resistance (R) Ω

R=

1 Ω =

R = ρ

ρ = resistivity

series circuits

Ohm’s Law V = IR

resistance in series

RT = = R1 +R2 +….RN

resistance in parallel

∑

=

capacitors in series

∑

=

capacitors in parallel

CT = = C1 +C2 + CN

electric energy

energy = (kwatts) (hrs)

electric power

P = ΔVI P=I2R P =

Joule heat = I2R

charging RC circuits

VC= Vo(1- e-1/τ

) τ = RC (time constant)

I(t) = e ≈ 2.718

Discharging RC circuits

VC = Vo ( e-t/τ

)