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Unformatted text preview: Circular Uniform Motion • Distinguish speed v (a scalar) from velocity vector v (a vector). • Uniform motion keeps velocity constant: linear motion • Uniform circular motion keeps speed constant (circular motion) c circlecopyrt L.Frommhold . – p.20/14 Centripetal Acceleration • Acceleration is change of velocity per change of time, vector a = vector v 2 vector v 1 t 2 t 1 = Δ vector v Δ t for Δ t → , but not Δ v/ Δ t ! • Note that for small time steps Δ t the vector Δ vector v ⊥ vector v and a c =  Δ vector v  Δ t ≈ v Δ θ Δ t = v 2 r because r · Δ θ = Δ ℓ = v Δ t c circlecopyrt L.Frommhold . – p.19/14 Uniform Circular Motion • Measure angles in radian units (“rad”) 360 ◦ equals 2 π = 6.283. . . radians Length of the arc equals r · Δ θ Revolutions per time f = (1 / 2 π ) (Δ θ/ Δ t ) Duration of a revolution T = 1 /f • Uniform circular motion is accelerated (!) motion, even though v = const . The point is that the vector vector v changes direction all the time. • Velocity vector and acceleration are at right angles. • The magnitude of centripetal acceleration is given by a c = v 2 r = (2 πf ) 2 r = 2 πf v = 2 π v T etc....
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This note was uploaded on 10/21/2009 for the course PHYSICS 30 taught by Professor Dr.lotharfrommhold during the Spring '09 term at University of Texas.
 Spring '09
 Dr.LotharFrommhold
 Physics, Acceleration, Circular Motion

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