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Equations Of Motion |
v = v0 + at
x = x0 + v0t + ½at2
v2 = v02 + 2a(x − x0) v̅ = ½(v + v0)
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Newton's 2nd Law |
∑ F = m a
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Dry Friction |
ƒ μN
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Centripetal Accel. |
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ac = − ω2r
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Impulse |
J = Δt
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J = | | F dt |
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Impulse-Momentum |
Δt = mΔv
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| F dt = Δp |
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Work |
W = Δs cos θ
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W = | | F · ds |
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Work-Energy |
Δs cos θ = ΔE
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| F · ds = ΔE |
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General Potential Energy |
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ΔU = − | | F · ds |
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F = − ∇U
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Gravitational Potential Energy |
ΔUg = mgΔh
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Power |
= |
ΔW | Δt |
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Power-Velocity
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= v cos θ
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P = F · v
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Angular Velocity |
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v = ω × r
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Angular Acceleration |
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a = α × r − ω2 r
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Equations Of Rotation |
ω = ω0 + αt
θ = θ0 + ω0t + ½αt2
ω2 = ω02 + 2α(θ − θ0)
ω̅ = ½(ω + ω0)
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Newton's second law of rotational motion |
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∑ τ = I α
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Torque |
τ = rF sin θ
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τ = r × F
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Moment Of Inertia |
I = ∑ mr2
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I = |
| r2 dm |
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Rotational Motion |
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W = τ̅Δθ
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W = |
| τ · dθ |
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Rotational power |
P = τω cos θ
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P = τ · ω
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Rotational Kinetic Energy |
K = ½Iω2
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Angular Momentum |
L = mrv sin θ
L = r × p
L = I ω
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Newton's Law Of Universal Gravitation |
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Gravitational Field Surrounding a Point Mass |
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Potential Energy Surrounding a Point Mass |
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Gravitational Potential Surrounding a Point Mass |
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Elastic Potential Energy |
Us = ½kΔx2
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Period of a Simple Harmonic Oscillator |
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Period of a Simple Pendulum |
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Angular-Linear Frequency Relation |
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ω = 2pƒ |
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Pressure-Depth Relation for a Fluid of Uniform Density |
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P = P0 + ρgh
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Archimedes' Law of Buoyancy |
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B = ρgVdisplaced
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Mass Continuity |
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ρ1A1v1 = ρ2A2v2
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Volume Continuity |
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A1v1 = A2v2
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Bernoulli's Equation |
P1 + ρgy1 + ½ρv12 =
P2 + ρgy2 + ½ρv22 |
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Dynamic Viscosity |
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| = η |
Δvx | A | Δz |
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