Download - 2012 Physics Final Formula Sheet

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Page 1: 2012 Physics Final Formula Sheet

Distance length d meters

Velocity

ms

meters per second

v= Δd

Δt

meters per

second

Acceleration

2

ms

or mss

meters per

second squared

a= Δv

Δt

meters per

second squared

Force

2

kg ms⋅

or

mkgs

s

mass times acceleration

impulse divided

by time

F=ma

F= Δp

Δt

Newtons

Energy / Work 2

2

kg ms⋅

Joules

Work ( )2

mkg ms

⎛ ⎞⎜ ⎟⎝ ⎠

Force times

distance

W F d= ⋅

Joules

Gravitational Potential energy

(Joules)

( )2

mkg ms

⎛ ⎞⎜ ⎟⎝ ⎠

mass times gravity times

change in height

( )gPE mg h= Δ

Joules

Kinetic Energy

2mkg

s⎛ ⎞⎜ ⎟⎝ ⎠

one half mass times velocity

squared

21

2KE mv=

Joules

Power

2

3

kg ms⋅

2

m mkgs s

⎛ ⎞⎛ ⎞⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠

work divided by time

or

Force times velocity

WP Fvt

= =

Watts

Momentum

mkgs

⎛ ⎞⎜ ⎟⎝ ⎠

mass times velocity

p =m

v

Impulse

mkgs

⎛ ⎞⎜ ⎟⎝ ⎠

change in

momentum Δp= FΔt

Δp=mΔ

v

Page 2: 2012 Physics Final Formula Sheet

force mass linear momentum

Fmρ

===

torque moment of inertia angular momentum

IL

τ ===

Linear

Rotational

2 1

2 2

x xv

t t−=−

2 1

2 2t tθ θϖ −=

2 1

2 2

v vat t−=−

2 1

2 2t tϖ ϖα −=

20 0

12

x x v t at= + + 20 0

12

t tθ θ ϖ α= + +

( )2 20 02v v a x x= + − ( )2 2

0 02ϖ ϖ α θ θ= + −

0v v at= + 0 tϖ ϖ α= +

Calculating Moment of Inertia

2 2 2

1 1 2 2 3 3 ...I m r m r m r= + + +

Linear Force Rotational Force

F ma

Ftρ

=Δ=Δ

( )sinF rILt

τ θτ α

τ

=

=Δ=Δ

Linear Kinetic Energy Rotational Kinetic Energy

212

KE mv=

212

KE Iϖ=

Linear and Rotational Kinetic Energy (for a body with both linear motion and spin)

2 21 12 2

KE mv Iϖ= +

Linear Momentum Angular Momentum

mvρ =

L Iϖ=

Page 3: 2012 Physics Final Formula Sheet

Angular Conversions:

1800 = π radians Conversions from angular to linear for a point on a rotating object

tan

x rv ra r

θϖα

===

Radial Acceleration

2

radial cpva ar

= =

Center of Mass

1 1 2 2 3 3

1 2 3

1 1 2 2 3 3

1 2 3

1 1 2 2 3 3

1 2 3

.........

......

...

cm

cm

cm

x m x m x mx

m m my m y m y m

ym m m

zm z m z mz

m m m

+ + +=+ + ++ + +

=+ + +

+ + +=+ + +

Page 4: 2012 Physics Final Formula Sheet

Waves: True of any wave: ! = !" Hertz = !

!"#$%& Period:

! = 1!

Speed of sound in air: ! = 343!! Intensity of Sound:

! = !! !!"!

!!!!

Intensity of Sound over distance:

! = !4!!!!

Intensity Level of Sound: !" = 10(!"#$ + 12) Speed of Light In Vacuum: 3.00 x 108 m/s

Index of Refraction:

n = c

v= speed of light in vacuum

speed of light in specific medium

n1

n2

=sinθ2

sinθ1

Total Internal Reflection:

sinθ =

n2

n1

θ is the angle at which the ray of light will reflect rather than pass between the two mediums with the given refractive indices. Electricity: Charge of a single electron: -1.60 x 10-19 C Number of electrons in a single Coulomb: 6.25 x 1018 electrons Mass of a single electron: 9.10939 x 10-31 kg

Page 5: 2012 Physics Final Formula Sheet

Velocity of a wave: v = λf

Velocity of a transversal wave on a stretched cable:

v =FT

mL

⎛⎝⎜

⎞⎠⎟

Velocity of a Longitudinal Wave along a Solid Rod:

v = E

ρ

E is the elastic modulus of the material, and ρ is the density of the material

Velocity of a Longitudinal Wave through a liquid or gas:

v = B

ρ

B is the bulk modulus of the material, and ρ is the density of the liquid or gas

Energy of a Wave:

E = 2π 2 density of medium( ) area of wave front( ) velocity( ) time( ) frequency( )2 amplitude( )2 Power of a Wave:

P = Etime

=2π 2 density of medium( ) area of wave front( ) velocity( ) time( ) frequency( )2

amplitude( )2

time

P = 2π 2 density of medium( ) area of wave front( ) velocity( ) frequency( )2amplitude( )2

Intensity of a wave:

I = Parea

=2π 2 density of medium( ) area of wave front( ) velocity( ) frequency( )2

amplitude( )2

area

I = 2π 2 density of medium( ) velocity( ) frequency( )2amplitude( )2

Page 6: 2012 Physics Final Formula Sheet

Helpful formulas: Always true:

2 1

2 1

2 1

2 1

average

average

d dvt tv vat t

−=−−=−

True if acceleration is assumed to be constant:

( )

20 0

0 0

0

022

0

12

1 ( )21 ( )2

2 ( )

average

o

x x v t at

x x v v t

v v v

v v at

v v a x x

= + +

= + +

= +

= +

= + − Gravity:

2

2

32

9.81

ftgs

mgs

= −

= −

Free fall:

2v gh=

Vectors: A = Ax

2 + Ay2

Ax =A cosθ

Ay =A sinθ

θ = tan−1 AyAx

⎝⎜

⎠⎟

Ballistic Trajectory: Horizontal Launch Angle:

0

2012

x v t

y y gt

=

= −

General Launch Angle:

( )

( )0

20 0

cos

1sin

2

x v t

y y v t gt

θ

θ

=

= + −

Time to peak 0 sinvg

θ=

Page 7: 2012 Physics Final Formula Sheet

Newton's 2nd Law: F ma=ur r

in Newtons

( )21

kg mN

s=

Newton's 3rd Law: F1

= −F2

m1a1 =m2(−a2)

Units of mass: kilogram, slug

Units of weight:

2

2

kg mnewtons

s

slug ftpounds

s

=

=

Friction: k k

s s

f Nf N

µµ

==

Ideal Spring: F kx=

Ideal String and Pulley: Tension is constant throughout the string. A pulley changes the direction of the tension.

Centripetal Acceleration:

2

2

cp

cp

varvf mr

=

=

Angle at which a car can drive along a banked curve even if there’s no friction:

tanθ = v 2

gr

Linear and rotational speed:

revolutionstime

⎛⎝⎜

⎞⎠⎟

2π1 revolution

⎛⎝⎜

⎞⎠⎟= Angular Velocity

Page 8: 2012 Physics Final Formula Sheet

Kinetic Energy (in Joules):

212

KE mv=

Work (in Joules): W Fd= Work at an angle (in Joules):

( cos )W F dθ= Total Work (in Joules):

220

1 12 2

W mv mv= −∑

( )1 1J N m=

Momentum: p mv=r r

Impulse:

Δρ= mΔv

Δρ= FΔt

Power (in Watts):

WP Fvt

= =

11

746 1

JWs

W hp

=

= Potential Energy due to gravity: gU mgh=

Potential Energy in a compressed or stretched spring:

212gU kx=

Conservation of Energy due to gravity: i i f fU K U K+ = +

1 12 2i i f fmgh mv mgh mv+ = +

Page 9: 2012 Physics Final Formula Sheet

Elastic Collisions:

1 1 2 2 1 1 2 2

2 2 2 21 1 2 2 1 1 2 2

1 1 1 12 2 2 2

i i f f

i i f f

m v m v mv m v

mv m v mv m v

+ = +

+ = +

Inelastic Collisions:

1 1 2 2 1 1 2 2

2 2 2 21 1 2 2 1 1 2 2

1 1 1 12 2 2 2

i i f f

i i f f

m v m v mv m v

mv m v mv m v

+ = +

+ ≠ +

Completely Inelastic Collisions:

1 1 2 2 1 2

2 2 21 1 2 2 1 2

( )1 1 1 12 2 2 2

i i f

i i f

m v m v m m v

mv m v m m v

+ = +

⎛ ⎞+ ≠ +⎜ ⎟⎝ ⎠

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