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Linear vs Angular - Δx = x x Δθ = θ θ v av = Δx/Δt...

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LINEAR VERSUS ANGULAR PHYSICS Parameter Linear Units Angular Units Time t s t s Position x, y m θ rad Displacement m rad Velocity, Average m/s rad/s Velocity, Instantaneous v = lim Δx/Δt m/s ω = lim Δθ/Δt rad/s Acceleration, Average Acceleration, Instantaneous a = lim Δv/Δt α = lim Δω/Δt 2π rads = 360 degrees For Constant Acceleration Position m rad Position x = 1/2 (v0 + v)t θ = 1/2 (ω0 + ω)t Velocity m/s rad/s Velocity m/s rad/s Acceleration a = constant α = constant Force/Torque Force, F Torque, τ = Force*(moment arm) Nm Mass/Moment of Inertia m kg Newton's Second Law N Nm Newton's First Law Work W = F*s = Fcosφs J=Nm W = τ Δθ Nm Kinetic Energy J J Power W=J/s W Momentum/Angular Momentum p = mv kgm/s L = I*ω Impulse J = FΔt = Δp Ns Converting Angular to Linear:
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Unformatted text preview: Δx = x - x Δθ = θ - θ v av = Δx/Δt = (x- x )/(t- t ) ω av = Δθ/Δt = (θ- θ )/(t - t ) a av = Δv/Δt = (v- v )/(t- t ) m/s 2 α av = Δω/Δt = (ω- ω )/(t- t ) rad/s 2 m/s 2 rad/s 2 x = v t+1/2at 2 θ = ω t+1/2αt 2 v = v +at ω = ω +αt v 2 = v 2 + 2aΔx ω 2 = ω 2 + 2αΔθ m/s 2 rad/s 2 N=kgm/s 2 I (=MR 2 for point mass) kgm 2 F net = ma =Δp/Δt τ net = Iα = ΔL/Δt If F net =0 then v=0 or constant If τ net then ω=0 or constant K = 1/2 mv 2 K = 1/2 I ω 2 P av = ΔW/Δt P av = ΔW/Δt = τω kgm 2 /s s = rθ; v=rω; a tan =rα, a c =v 2 /r,a rad =rω 2...
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