2012 Physics Final Formula Sheet

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Transcript of 2012 Physics Final Formula Sheet

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21
I L


1 2
( )2 2 0 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
τ θ τ α
21 2
KE mv=
21 2
KE Iϖ=
Linear and Rotational Kinetic Energy (for a body with both linear motion and spin)
2 21 1 2 2
KE mv Iϖ= +
L Iϖ=
Angular Conversions:
1800 = π radians Conversions from angular to linear for a point on a rotating object
tan
θ ϖ α
= =
1 2 3
1 2 3
1 2 3
m m m y m y m y m
y m m m
m m m
!"#$%& Period:
! = 1 !
! = ! ! !!"!
! !!!
! = ! 4!!!!
Intensity Level of Sound: !" = 10(!"#$ + 12) Speed of Light In Vacuum: 3.00 x 108 m/s
Index of Refraction:
n1
n2
= sinθ2
sinθ1
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
Velocity of a wave: v = λf
Velocity of a transversal wave on a stretched cable:
v = FT
m L
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 = E time
= 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( )2 amplitude( )2
Intensity of a wave:
I = P area
= 2π 2 density of medium( ) area of wave front( ) velocity( ) frequency( )2
amplitude( )2
area
I = 2π 2 density of medium( ) velocity( ) frequency( )2 amplitude( )2
Helpful formulas: Always true:
−= − −= −
( )
v v v
v v at
= + +
= + +
= +
= +




0
θ
θ
θ=
in Newtons
Units of weight:
Ideal Spring: F kx=
Ideal String and Pulley: Tension is constant throughout the string. A pulley changes the direction of the tension.
Centripetal Acceleration:
=
=
Angle at which a car can drive along a banked curve even if there’s no friction:
tanθ = v 2
21 2
KE mv=
Work (in Joules): W Fd= Work at an angle (in Joules):
( cos )W F dθ= Total Work (in Joules):
22 0
Impulse:
Potential Energy in a compressed or stretched spring:
21 2gU kx=
Conservation of Energy due to gravity: i i f fU K U K+ = +
1 1 2 2i i f fmgh mv mgh mv+ = +
Elastic Collisions:
1 1 2 2 1 1 2 2
2 2 2 2 1 1 2 2 1 1 2 2
1 1 1 1 2 2 2 2
i i f f
i i f f
mv m v mv m v
+ = +
+ = +
1 1 2 2 1 1 2 2
2 2 2 2 1 1 2 2 1 1 2 2
1 1 1 1 2 2 2 2
i i f f
i i f f
mv m v mv m v
+ = +
+ ≠ +
2 2 2 1 1 2 2 1 2
( ) 1 1 1 1 2 2 2 2
i i f
i i f
mv m v m m v
+ = +
+ ≠ +