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# 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

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