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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 = V
0
+ at
V
0
= Initial velocity of object
V = Final velocity of object
a = Accele­ration of object
t = Time
V2 = V
0
2 + 2aΔx
V
0
= Initial velocity of object
V = Final velocity of object
a = Accele­ration of object
Δx / Δy = Change in position
Δx = V
0
t + ½at2
Δx / Δy = Change in position
V
0
= Initial velocity
t = Time
a = Accele­ration
F = ma
F = Force from object
m = Mass of object
a = Accele­ration of object
F
f
= μN
F
f
= 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 = m
V
- m
V0
FΔt = Δp = Impulse
m
V
= Final momentum
m
V0
= Initial momentum
m
Vbefore
- m
V0before
= m
Vafter
- m
V0after
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 - ½mV
0
2
W = Work done
m = Mass of object
V = Final velocity
V
0
= Initial velocity
U
g
= mgh
U
g
= Work done by gravity
m = Mass
g = Gravity
h / d = Height or distance traveled
F
S
= kx
F
S
= Force of spring (Restored Force)
k = Spring coefficient
x = Distance from equili­brium
W
S
= U
S
= ½kx2
W
S
= Work done by spring
k = Spring coefficient
x = Distance from equili­brium
KE = ½mV2
KE = Kinetic Energy
m = Mass
v = Velocity of object
KE + U
g
+ U
S
=
KE + U
g
+U
S
+ W
KE = Kinetic Energy (is the object moving?)
U
g
= Work done by gravity (is the object above where you set x = 0?)
U
S
= 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 = ω
0
+ αt
ω
0
= Angular initial velocity
ω = Angular final velocity
α = Angular acceleration
t = Time
ω2 = ω
0
2 + 2αθ
ω
0
= Angular initial velocity
ω = Angular final velocity
α = Angular acceleration
θ = Angular change in position
θ = ω
0
t + ½αt2
θ = Angular change in position
ω
0
= Angular initial velocity
t = Time
α = Angular accele­ration
V
T
= rω
V
T
= Tangential (Linear) velocity
r = Radius
ω = Angular final velocity
a
T
= rα
a
T
= Tangential (Linear) acceleration
r = Radius
α = Angular accele­ration
a
C
= V
T
2 / r
a
C
= Centri­petal acceleration
V
T
= Tangential (Linear) velocity
r = Radius
a
r
= rω2
a
r
= Radial Acceleration
r = Radius
ω = Angular velocity
τ = F
⊥
d
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
KE
C
= 1/2(I)ω2
KE
C
= 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
KE
R
= 1/2 I
P
ω2 = 1/2(I
COM
+ mhh)ω2
=1/2(m(V
COM
)2) + 1/2Iω2
KE
R
= Kinetic Rolling Energy
1/2(m(V
COM
)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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  • Published: 23rd October, 2020
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Comments

very well organized

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