Cheatography

# AP Physics Formulas (Kinematic) Cheat Sheet by ReSummit

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 objectV = Final velocity of objecta = Accele­ration of objectt = Time V2 = V`0`2 + 2aΔx V`0` = Initial velocity of objectV = Final velocity of objecta = Accele­ration of objectΔx / Δy = Change in position Δx = V`0`t + ½at2 Δx / Δy = Change in positionV`0` = Initial velocityt = Timea = Accele­ration F = ma F = Force from objectm = Mass of objecta = Accele­ration of object F`f` = μN F`f` = Force of frictionμ = Coeffi­cient of frictionN = 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 = Impulsem`V` = Final momentumm`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 doneF = Force appliedd = Distance travelled W = ΔKE = ½mV2 - ½mV`0`2 W = Work donem = Mass of objectV = Final velocityV`0` = Initial velocity U`g` = mgh U`g` = Work done by gravitym = Massg = Gravityh / d = Height or distance traveled F`S` = kx F`S` = Force of spring (Restored Force)k = Spring coefficientx = Distance from equili­brium W`S` = U`S` = ½kx2 W`S` = Work done by springk = Spring coefficientx = Distance from equili­brium KE = ½mV2 KE = Kinetic Energym = Massv = 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 velocityω = Angular final velocityα = Angular accelerationt = Time ω2 = ω`0`2 + 2αθ ω`0` = Angular initial velocityω = Angular final velocityα = Angular accelerationθ = Angular change in position θ = ω`0`t + ½αt2 θ = Angular change in positionω`0` = Angular initial velocityt = Timeα = Angular accele­ration V`T` = rω V`T` = Tangential (Linear) velocityr = Radius ω = Angular final velocity a`T` = rα a`T` = Tangential (Linear) accelerationr = Radiusα = Angular accele­ration a`C` = V`T`2 / r a`C` = Centri­petal accelerationV`T` = Tangential (Linear) velocityr = Radius a`r` = rω2 a`r` = Radial Accelerationr = Radiusω = Angular velocity τ = F`⊥`d τ = TorqueF`⊥` = Perpen­dicular Forcesd= 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 EnergyI = Moment of Inertia (Rotat­ional Moment / Rotational Intertia)ω = Angular velocity τ = Iα τ = TorqueI = 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 Energy1/2(m(V`COM`)2) = Sliding Equation1/2Iω2 = 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.

very well organized