Lecture_13

Lecture_13 - be zero Conservation of Energy If an object is...

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Energy of Rotation
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Rotational Energy Each piece of a rotating object carries a piece of kinetic energy All the objects move with the same angular velocity. Recall that So KE i = 1 2 m i v i 2 v i r i I = i m i r i 2 KE rot = i KE i = i 1 2 m i v i 2 = i 1 2 m i r i ) 2 = 1 2 ω 2 ( i m i r i 2 ) KE rot = 1 2 I ω 2 We could have guessed this just by substituting rotational quantities for translational quantities.
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Example Which has greater kinetic energy? Same angular speed I = 2 3 m R 2 I = 1 2 m R 2 I = 1 12 m R 2
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Total Kinetic Energy KE tot = 1 2 m v 2 + 1 2 I ω 2
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Torque and KE Recall Similarly This is the work-energy theorem for rotation Δ KE trans = F ¿ d Δ KE rot =τθ Note: Friction does no work on a rolling object. The point of contact with the surface (i.e. the point that friction acts on) is at rest so its angulate displacement will
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Unformatted text preview: be zero Conservation of Energy If an object is acted on by only conservative forces (or those non-conservative forces that do no work) then mechanical energy is conserved: Example: KE i + PE i = KE f + PE f 1 2 m v i 2 + 1 2 I i 2 + mgh i = 1 2 m v f 2 + 1 2 I f 2 + mgh f These will involve r 2 so we will be able to convert r to v. Example Rolling down a hill. Which one wins? Example How to make a yo-yo faster? Make radius larger Make radius smaller Add mass near rotation axis (yo-yo will be more like a sphere) Hollow out the center (yo-yo will be more like a cylindrical shell)...
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Lecture_13 - be zero Conservation of Energy If an object is...

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