3
x cm = 1 M m i x i i ∑ = m 1 x 1 + m 2 x 2 + m 3 x 3 + .... m 1 + m 2 + m 3 y cm = 1 M m i y i i ∑ = m 1 y 1 + m 2 y 2 + m 3 y 3 + .... m 1 + m 2 + m 3 K rot = 1 2 Iω 2 I = m i i ∑ r i 2 τ ≡ rF sin φ τ = dF = (r sin φ ) F Torque s = rθ v cm = Rω a cm = Rα K rolling = 1 2 I cm ω 2 + 1 2 Mv cm 2 K rolling = 1 2 I cm v cm r " # $ % & ' 2 + 1 2 Mv cm 2 K rolling = 1 2 I cm ω 2 + 1 2 M (rω ) 2 Angular Momentum L = I ω For a point particle L = mr 2 v t r " # $ % & ' = mrv t I = mr 2 I = m i r i 2 i ∑ NII : Ang Mom Ang Mom Con I = I cm + md 2 F net = Δp • A p = F g A = ρ f gd p = p o + ρ gd ρ = m V p o = p 1 or F 1 A 1 = F 2 A 2 T K = T C + 273.15 PV = Nk b T = nRT kB = 1.38 x 10 -23 J/K NA = 6.02 x 10 23 particles/mol R = 8.31 J/(mol K) W = − pdV V i V f ∫ p f V f γ = p i V i γ T f V f γ −1 = T i V i γ −1 ΔE th = W + Q Q = McΔT Q =± ML General Physics - Phy101 Final Prof. Bob Ekey Center of Mass Rotational Kinetic Energy Moment of Inertia Inertia for Unknown system Newton’s II law for Rotations Stable Equilibrium Conditions Pressure Pressure from fluid above an area A Total Pressure from fluid above an area A Net force from pressure Density Pascal’s Principle Temperature conversion Ideal Gas Law number of moles n = N/NA 1 st Law of Thermodynamics Work done on gas by environment Adiabatic Heat within one phase (W=0) Heat during phase change (W=0) τ net = τ i ∑ = I α F net = F i = 0 τ net = τ i ∑ ∑ = 0 p = F ⊥ A = F cos θ A I sys = I 1 + I 2 + I 3 + ... Kinetic Energy of a Rolling Body Kinetic Energy of a Rolling Body (no slip) Parallel Axis Theorem No Slip Conditions for Rolling Objects τ net = Δ L Δt = d L dt I for Point Particle I for Multiple Point Particles ! L f ∑ = ! L i ∑ γ = C p C V
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