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11 General Rotation ay

11 General Rotation ay - Chapter 11 Angular Momentum 1...

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1 Chapter 11 Angular Momentum
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2 Angular Momentum Linear momentum: p = mv Angular momentum: L = I ω Σ τ = I α = Σ F = ma = dL dt dp dt The rate of change of angular momentum of a particle is equal to the net torque applied to it.
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3 Vector Cross Product C = A x B = AB sin θ
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4 Cross Product A = A x i + A y j + A z k B = B x i + B y j + B z k i j k A x B = A x A y A z B x B y B z = ( A y B z – A z B y ) i + ( A z B x – A x B z ) j + ( A x B y – A y B x ) k
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5 L vector is parallel to ω vector
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6
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7 τ ext = dL dt The total angular momentum of a rotating body remains constant if the net external torque acting on it is zero . is valid only when torque and angular momentum are calculated with respect to center of mass!
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8 Conceptual Example A person stands, hands at the side, on a platform that is rotating at a rate of 1.30 rev/s. If the person now raises his arms to the horizontal position, the speed of rotation decreases to 0.80 rev/s. ( a ) Why does this occur? ( b ) By what factor has the moment of inertia of the person changed?
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9 When the skater pulls her arms in, she is decreasing her moment of inertia.
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10 Conceptual Example Spinning bicycle wheel. A student is holding a spinning bicycle wheel standing on a stationary frictionless turntable. What will happen if the student suddenly flips the bicycle wheel over so that it is spinning in the opposite direction?
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