Cheatography

# Physics Final Cheat Sheet Cheat Sheet by brandenz1229

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### Chapter 2: Motion along A Straight Line

 s = speed t = time Total Distance x`f`+x`i` One Dimens­ional Motion Distance d = s⋅t Displa­cement x`f`-x`i` Speed (x`f`+x`i`) / (t`f`+`t`i`) Not Constant Velocity Average Velocity (x`f`-x`i`) / (t`f`-`t`i`) x↑: v+ x↓: v- x→: v=0 a+: v↑ a-: v↓ a=0: v→ Instan­taneous Accele­ration (v`f`-v`i`) / (t`f`-`t`i`) Constant Accele­ration in 1D V`f` = V`i` + (a⋅t) Constant Accele­ration Final Distance X`f`= 1/2(V`f`-V`i`) ⋅ t X`f`= X`i` + (V`i`⋅ t) + 1/2(a ⋅ t) a = (V`f`-V`i`) / t t = (V`f`-V`i`) / a V`f` = V`i`⋅ a2 V`f`2 = V`i`2 + 2⋅a (x`f`-x`i`) G`y` = -9.8 m/s

### Chapter 14: Periodic Motion

 Angular Frequency w = 2πf 2π/T Frequency f = 1 / T Period T = 1 / f Restoring Force F`x` = -kx Simple Harmonic Motion k = Spring Constant x = displa­cement m = mass Displa­cement as function of time x = Acos(wt + Θ) Velocity as function of time v = -wAsin(wt + Θ) Accele­ration as function of time a = -w2Acos(wt + Θ) x`max` = A [Ampli­tude] -x`max` = A [Ampli­tude] v`max` = wA -v`max` = wA a`max` = w2A -a`max` = w2A Equation for Simple Harmonic Motion a`x = - (k/m) x k = restoring force Angular Frequency for SHM w = √k/m Frequency for SHM f = w/2π f = 1/2π√k/m Period for SHM T = 1/f T = 2π/w T = 2π√m/k Total Mechanical Energy (Constant) E = 1/2mv`x`2 + 1/2kx2 E = 1/2kA2

### Chapter 6: Work and Kinetic Energy

 1km = 1000m 1 kg = 1000g Dot Product P = Power A⋅B = (A`i`⋅B`i`)+(A`j`⋅B`j`) t = s Work = Force ⋅ distance W = F`x`⋅ distance W = F⋅cosΘ­⋅di­stance K`E`: 1/2⋅m⋅v2 U = m⋅g⋅h W`total` = K`E``f` - K`E``i` W`x` = F (cosΘ)⋅s || W`y` = F (sinΘ)⋅s Constant Speed Friction (opposite) = cos(180o) P = F⋅v P = (W/t) P`av`= ΔW / Δt [Average Power] if F→ & s← = - W if F↓ & s→ = 0 if F→ & s→ = W Force Required to Stretch a spring F`x` = k ⋅ x

### Chapter 13: Newton's Law of Gravit­ation

 G`E`= 6.67⋅10-11 Earth Gravity Constant R`E`= 6.38⋅106 m Earth Radius M`E`= 5.972⋅1024 kg Mass of Earth g = 9.8 m/s; a`g` = 9.8 m/s r - R`E` = h F`g` = (G`E`⋅m`1`⋅m`2`) / (r2) F`g` = m ⋅ a w = m⋅g s = r - R`E` cosΘ Gravit­ation and Spheri­cally Symmetric Bodies F`g` = (G`E`⋅m`E`⋅m) / (r2) Weight of the body at Earth's Surface w = F`g` = (G`E`⋅m`E`⋅m) / (R`E`2) Accele­ration due to Gravity g = (G`E`⋅m`E`) / (R`E`2) Velocity of Earth V`E`= 4/3πR`E`2 = 1.08⋅1021 m3 Gravit­ational Potential Energy U = -(G`E`⋅m`E`⋅m) / (r) WorkDone by Gravity W`grav` = m⋅g(r`1`-r`2`) W`grav` = Gm`E`⋅m ⋅ (r`1`-r`2`) / (r`1`⋅r`2`) W`grav`= Gm`E`⋅m ⋅ (r`1`-r`2`) / (R`E`2) [if the body stays close to Earth] Speed of the Satellite v = √(G⋅m`E` / r) Period of Circular Orbit T = (2πr / v) T = 2πr3/2/√G⋅m`E` T = 2πr √(r / G⋅m`E`) Point Mass Outside a Spherical Shell U`i`= - Gm⋅m`i` / s Apparent weight ; Earth's Rotation w`0` = true weight of object F = force exerted by spring scale F + w`0` = net force on object w = apparent weight = opposite of F centri­petal accele­ration` w`0`- F = (mv2 / R`E`) w = w`0` - (mv2 / R`E`) freefall accele­ration g = g`0` - (v2/ R`E`) Black Holes P = Density P = M / v v = 4/3πR3 c = speed of light in the vaccum Schwar­dzs­child Radius R`s` = 2GM / c2 c = √2GM / R`S`

### Chapter 7: Potential Energy, Energy Conser­vation

 Y-axis E = Mechanical Energy W`grav` = F ⋅ s = w(y`1`-y`2`) W`grav`=(m⋅g⋅y`1`)-(m⋅g⋅y`1`) W`grav`=U`grav,1` - U`grav,2` W`grav` = -Δ U`grav` Conser­vation of Mechanical Energy K`f`-K`i` = U`grav,1` - U`grav,2` K`i`+U`grav,1`=K`f`+U`grav,2` E = K + U`grav` = constant (if gravity does work) When other forces than Gravity do work W`other` + W`grav` = K`f` - K`i` Elastic Potential Energy U`el` = 1/2kx2 Work Done a Spring W = 1/2kx`2`2 - 1/2kx`1`2 If Elastic does work, total mechanical energy is stored K`i`+U`el,1`=K`f`+U`el,2` Situations with Both Gravit­ational and Elastic Potential Energy K`1`+U`1`+W`other`=K`2`+U`2` The work done by all forces other than the gravit­ational force or elastic force equals the change in total mechanical energy E = K + U of the system The Law of Conser­vation of Energy ΔU`int` = -W`other` ΔU`int` = internal energy Force and Potential Energy F`x`(x) = - dU(x) / dx

### Chapter 14: Periodic Motion (cont.)

 The Simple Pendelum (TSP) L = pendulum length Angular Frequency TSP w = √k/m w = √mg / L /m w = √g/L Frequency TSP f = w/2π f = 1/2π √g/L Period TSP T = 2π/w T = 1/f T = 2π√L/g The Physical Pendulum (TPP) L = angular momentum L = mvr w = Angular Velocity w = ΔΘ / Δt (I)nertia = L / w Angular Frequency TPP w = √mgd / I Period TPP T = 2π √ I / mgd Damped Oscill­ation b = Damping Constant Displace of Damped x = Ae-b(2m)t cost (wt + Θ) Angular Frequency of Damped w' = √ (k/m) - (b2 / 4m2) Force Oscill­ations and Resonance F`max` = Maximum Driving Force k = constant restoring force w`d` = Driving Angular Frequency A = F`max` / √(k-mw`d`2)2 + b2w`d`2