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AP Physics Formulas (Kinematic) Cheat Sheet by

Some physics formulas that will be useful in kinematics. Not a truly complete list of formulas though, as some things are missing.I can't think of any more formulas for this cheat sheet though, so suggestions on what to add would be helpful.

Kinematics 2D Motion

V = V0 + at
V0 = Initial velocity of object
V = Final velocity of object
a = Accele­ration of object
t = Time
V2 = V02 + 2aΔx
V0 = Initial velocity of object
V = Final velocity of object
a = Accele­ration of object
Δx / Δy = Change in position
Δx = V0t + ½at2
Δx / Δy = Change in position
V0 = Initial velocity
t = Time
a = Accele­ration
F = ma
F = Force from object
m = Mass of object
a = Accele­ration of object
Ff = μN
Ff = Force of friction
μ = Coeffi­cient of friction
N = Normal force
Note: Some formulas may involve BOTH the x and y direct­ions, as well as incorp­orate other formulas outside kinema­tics.

Momentum

FΔt = Δp = mV - mV0
FΔt = Δp = Impulse
mV = Final momentum
mV0 = Initial momentum
mVbefore - mV0be­fore = mVafter - mV0after
Note: Momentum is ALWAYS conserved. You may need to note that the momentum before is equal to the momentum after.

Energy

W = Fd
W = Work done
F = Force applied
d = Distance travelled
W = ΔKE = ½mV2 - ½mV02
W = Work done
m = Mass of object
V = Final velocity
V0 = Initial velocity
Ug = mgh
Ug = Work done by gravity
m = Mass
g = Gravity
h / d = Height or distance traveled
FS = kx
FS = Force of spring (Restored Force)
k = Spring coefficient
x = Distance from equili­brium
WS = US = ½kx2
WS = Work done by spring
k = Spring coefficient
x = Distance from equili­brium
KE = ½mV2
KE = Kinetic Energy
m = Mass
v = Velocity of object
KE + Ug + US =
KE + Ug +US + W
KE = Kinetic Energy (is the object moving?)
Ug = Work done by gravity (is the object above where you set x = 0?)
US = Work done by spring (is a spring involved?)
W = Friction (did energy go to friction?)
Note: Energy is SOME­TIMES conserved depending on the situation. Inel­astic collisions cannot apply the conser­vation of energy because of the loss of energy. However, you can apply the conser­vation of energy for elas­tic collis­ions.
 

Rotational Motion

ω = ω0 + αt
ω0 = Angular initial velocity
ω = Angular final velocity
α = Angular acceleration
t = Time
ω2 = ω02 + 2αθ
ω0 = Angular initial velocity
ω = Angular final velocity
α = Angular acceleration
θ = Angular change in position
θ = ω0t + ½αt2
θ = Angular change in position
ω0 = Angular initial velocity
t = Time
α = Angular accele­ration
VT = rω
VT = Tangential (Linear) velocity
r = Radius
ω = Angular final velocity
aT = rα
aT = Tangential (Linear) acceleration
r = Radius
α = Angular accele­ration
aC = VT2 / r
aC = Centri­petal acceleration
VT = Tangential (Linear) velocity
r = Radius
ar = rω2
ar = Radial Acceleration
r = Radius
ω = Angular velocity
τ = Fd
τ = Torque
F = Perpen­dicular Forces
d= Distance from Pivot Point
I = Σmr^2
I = Moment of Inertia (Rotat­ional Moment / Rotational Intertia)
Σmr2 = Total of each Mass x Radius Squared
KEC = 1/2(I)ω2
KEC = Kinetic Circular Energy
I = Moment of Inertia (Rotat­ional Moment / Rotational Intertia)
ω = Angular velocity
τ = Iα
τ = Torque
I = Moment of Inertia (Rotat­ional Moment / Rotational Intertia)
α = Angular accele­ration
KER = 1/2 IPω2 = 1/2(ICOM + mhh2
=1/2(m(VCOM)2) + 1/2Iω2
KER = Kinetic Rolling Energy
1/2(m(VCOM)2) = Sliding Equation
1/2Iω2 = Rotation Equation
l = mrω
l = Momentum of a particle
L = Iω
L = Momentum of a rigid body (not a particle)
NOTE:
- You may need to consider that ω = dθ / dt and α = dω / dt.
- Account for all objects rotating the pivot point when calcul­ating I.
- Momentum is ALWAYS conserved.

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