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W10.3 - Physics for Scientists Engineers 1 Lecture 36...

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March 18, 2008 Physics for Scientists&Engineers 1 1 Physics for Scientists & Physics for Scientists & Engineers 1 Engineers 1 Lecture 36
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March 18, 2008 Physics for Scientists&Engineers 1 2 Review: Torque Review: Torque ! ! = ! r " ! F
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March 18, 2008 Physics for Scientists&Engineers 1 3 Review: Angular Momentum Review: Angular Momentum We start by defining the angular momentum of a point particle The magnitude of the angular momentum is given by Angular momentum and torque: For rigid objects (and only for them): ! L = ! r ! ! p L = rp sin ! d dt ! L = ! ! ! L = I ! !
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March 18, 2008 Physics for Scientists&Engineers 1 4 Conservation of L Conservation of L If the net torque is zero, then Angular momentum is conserved The conservation of angular momentum has many interesting consequences Gyroscopes Divers Dancers Ice-skaters… if ! ! net = 0 " ! L = constant " ! L ( t ) = ! L ( t 0 ) # ! L 0 I ! ! = I 0 ! ! 0
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March 18, 2008 Physics for Scientists&Engineers 1 5 Death of a Star Death of a Star If the iron core of a dying star initially spins with a rotation frequency of f 0 = 3.20 s -1 , and if the core’s radius decreases during the collapse by a factor of 22.7, what is the angular velocity of the iron core at the end of the collapse,
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