20 - Moment of Inertia

20 - Moment of Inertia - Rotational kinematics Read: 11.1,...

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Rotational kinematics Read: 11.1, 12.1 – 12.3 Handout, problems 3, 5, 7
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The further out - the faster (this goes back to the record cartoon) s r θ • Rotational variables and linear variables are related. • From the definition of the radian sr T ds v dt = d r dt θ = T vr
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Where is a R greatest on a merry-go-round? AB
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Where is a R greatest on a merry-go-round? 2 T R v a r = T - for tangential T but vr = ω 2 R ar ω ⇒= furthest out
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s r θ • Rotational variables and linear variables are related. T vr T T dv a dt = d r dt ω = T ar ⇒= α Connections
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Remember: tangential and radial (centripetal) acceleration R = + T aa a
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Remember: What if I speed up and change direction? RT =+ aa a a R a T a 22 + aa a = changes direction changes speed
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See the magic! Start with linear kinematic equation: fi vva t =+ But: ff vr = ω ii = ω ar = α rrr t →ω=ω+α t ⇒ω =ω +α
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See the magic! fi t ω =ω +α vva t =+ ( ) 1 if 2 tt ∆θ = ω = ω + ω ( ) 1 2 xv t vvt ∆= = + 2 1 i 2 ∆θ=ω + α 2 1 i 2 t a t ∆= + 22 2 ω =ω + α∆θ 2 vv a x =+∆ ⇔ Note: Only valid if angular acceleration is constant
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20 - Moment of Inertia - Rotational kinematics Read: 11.1,...

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