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
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=
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
+ + +=+ + ++ + +
=+ + +
+ + +=+ + +
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
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
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=
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
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+ = +
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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