Lecture19 - Angular Momentum Linear motion Angular motion...

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Angular Momentum Linear motion : Linear Momentum p = mv dp dt F = Angular motion : Angular Momentum L Because of the equivalence between m I v ω L = I ω Similarly: dp dt F = dL dt τ = Demo : τ = Ι α d ω dt = Ι = d dt ( Ι ω ) dL dt = • L is a vector same direction ω L ω Definition
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Conservation of Angular Momentum Conservation Linear Momentum : (If F ext = 0) p in = p fin Ι ω in = Ι ω fin NOTE : • L = cost. unelss we act with a τ = 0 • If τ =0 but F = 0 L is still conserved L in = L fin Conservation Angular Momentum : (If τ ext = 0 dL/dt =0)
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ω in < ω in Example: John is rotating with an angular velocity of ω 0 . What happens if he pulls his arm closer? τ ext = 0 L is conserved! L= Ι ω ω fin = ω in I 0 I f Ι fin ω fin = Ι 0 ω in L in = L fin To calculate Ι we can think of the problem as: R m m Ι 0 = m (R/2) 2 + m (R/2) 2 = mR 2 /2 ω fin = ω in R 2 x 2 x > R x < R ω fin > ω in ω fin < ω in Slow down fasters Ι f = m (x/2) 2 + m (x/2) 2 = mx 2 /2 x
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Example: You are holding in your arms a spinning wheel, while sitting on a rotatable platform. What happens when you flip over wheel? L in wheel L fin s L fin wheel start end L in = L wheel,0 L fin = L wheel,f + L stud,f L in = L fin No external torques acting on the student- stool system L is conserved L wheel,0 = - L wheel,f L stud = 2 L wheel,0 Student will start spinning in same direction the wheel was originally spinning
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A disk rotates of mass M and radius R rotates around an axis through its CM. A car of mass m moves slowly from the rim of the disk toward its center. If the angular speed of the system is 2rad/s when the car is at the rim:
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Lecture19 - Angular Momentum Linear motion Angular motion...

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