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Chapter 2: Motion along A Straight Lines = speed | t = time | Total Distance | xf+xi | One Dimensional Motion | Distance | d = s⋅t | Displacement | xf-xi | Speed | (xf+xi) / (tf+ti`) | Not Constant Velocity | Average Velocity | (xf-xi) / (tf-ti`) | x↑: v+
x↓: v-
x→: v=0 | a+: v↑
a-: v↓
a=0: v→ | Instantaneous Acceleration | (vf-vi) / (tf-ti`) | Constant Acceleration in 1D | Vf = Vi + (a⋅t) | Constant Acceleration Final Distance | Xf= 1/2(Vf-Vi) ⋅ t | Xf= Xi + (Vi⋅ t) + 1/2(a ⋅ t) | a = (Vf-Vi) / t | t = (Vf-Vi) / a | Vf = Vi⋅ a2 | Vf2 = Vi2 + 2⋅a (xf-xi) | Gy = -9.8 m/s |
Chapter 14: Periodic MotionAngular Frequency | w = 2πf
2π/T | Frequency | f = 1 / T | Period | T = 1 / f | Restoring Force | Fx = -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) | xmax = A [Amplitude] | -xmax = A [Amplitude] | vmax = wA | -vmax = wA | amax = w2A | -amax = 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 = 1/2mvx2 + 1/2kx2 | | | E = 1/2kA2 |
| | Chapter 6: Work and Kinetic Energy1km = 1000m | 1 kg = 1000g | Dot Product | P = Power | A⋅B = (Ai⋅Bi)+(Aj⋅Bj) | t = s | Work = Force ⋅ distance | W = Fx⋅ distance | W = F⋅cosΘ⋅distance | KE: 1/2⋅m⋅v2 | U = m⋅g⋅h | Wtotal = KEf - KEi | Wx = F (cosΘ)⋅s || Wy = F (sinΘ)⋅s | Constant Speed | Friction (opposite) = cos(180o) | P = F⋅v | P = (W/t) | Pav= ΔW / Δt [Average Power] | if F→ & s← = - W | if F↓ & s→ = 0 | if F→ & s→ = W | Force Required to
Stretch a spring | Fx = k ⋅ x |
Chapter 13: Newton's Law of GravitationGE= 6.67⋅10-11 | Earth Gravity Constant | RE= 6.38⋅106 m | Earth Radius | ME= 5.972⋅1024 kg | Mass of Earth | g = 9.8 m/s; ag = 9.8 m/s | r - RE = h | Fg = (GE⋅m1⋅m2) / (r2) | Fg = m ⋅ a | w = m⋅g | s = r - RE cosΘ | Gravitation and Spherically
Symmetric Bodies | Fg = (GE⋅mE⋅m) / (r2) | Weight of the body at Earth's Surface | w = Fg = (GE⋅mE⋅m) / (RE2) | Acceleration due to Gravity | g = (GE⋅mE) / (RE2) | Velocity of Earth | VE= 4/3πRE2 = 1.08⋅1021 m3 | Gravitational Potential Energy | U = -(GE⋅mE⋅m) / (r) | WorkDone by Gravity | Wgrav = m⋅g(r1-r2) | Wgrav = GmE⋅m ⋅ (r1-r2) / (r1⋅r2) | Wgrav= GmE⋅m ⋅ (r1-r2) / (RE2) | [if the body stays close to Earth] | Speed of the Satellite | v = √(G⋅mE / r) | Period of Circular Orbit | T = (2πr / v) | T = 2πr3/2/√G⋅mE | T = 2πr √(r / G⋅mE) | Point Mass Outside
a Spherical Shell | Ui= - Gm⋅mi / s | Apparent weight
; Earth's Rotation | w0 = true weight of object | F = force exerted by spring scale | F + w0 = net force on object | w = apparent weight = opposite of F | centripetal acceleration` | w0- F = (mv2 / RE) | | | w = w0 - (mv2 / RE) | freefall acceleration | g = g0 - (v2/ RE) | Black Holes | P = Density | P = M / v | v = 4/3πR3 | c = speed of light in the vaccum | Schwardzschild Radius | Rs = 2GM / c2 | c = √2GM / RS |
| | Chapter 7: Potential Energy, Energy ConservationY-axis
E = Mechanical Energy | Wgrav = F ⋅ s = w(y1-y2) | Wgrav=(m⋅g⋅y1)-(m⋅g⋅y1) | Wgrav=Ugrav,1 - Ugrav,2 | Wgrav = -Δ Ugrav | Conservation
of Mechanical Energy | Kf-Ki = Ugrav,1 - Ugrav,2 | Ki+Ugrav,1=Kf+Ugrav,2 | E = K + Ugrav = constant
(if gravity does work) | When other forces
than Gravity do work | Wother + Wgrav = Kf - Ki | Elastic Potential Energy | Uel = 1/2kx2 | Work Done a Spring | W = 1/2kx22 - 1/2kx12 | If Elastic does work,
total mechanical energy
is stored | Ki+Uel,1=Kf+Uel,2 | Situations with Both Gravitational
and Elastic Potential Energy | K1+U1+Wother=K2+U2 | 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 | ΔUint = -Wother
ΔUint = internal energy | Force and Potential Energy | Fx(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 | Fmax = Maximum Driving Force | k = constant restoring force | wd = Driving Angular Frequency | A = Fmax / √(k-mwd2)2 + b2wd2 |
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