Angular Momentum of Systems of Particles

Angular Momentum of Systems of Particles - for linear...

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Angular Momentum of Systems of Particles Consider a rigid body rotating about an axis. Each particle in the body moves in a circular path, implying that the angle between the velocity of the particle and the radius of the particle is 90 o . If there are n particles, we find the total angular momentum of the body by summing the individual angular moments: L = l 1 + l 2 + ... + l n Now we express each l in terms of the particle's mass, radius and velocity: L = r 1 m 1 v 1 + r 2 m 2 v 2 + ... + r n m n v n We now substitute σ for v using the equation v = σr : L = m 1 r 1 2 σ 1 + m 2 r 2 2 σ 2 + ... + m n r n 2 σ n However, in a rigid body, each particle moves with the same angular velocity. Thus: L = ( mr 2 ) σ = Here we have a concise equation for the angular momentum of a rigid body. Note the similarity to our equation of p = mv
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Unformatted text preview: for linear momentum. From this equation for a rigid body we can also generate a statement relating external torque and total angular momentum: ext = Just as an external force changes the total linear momentum of a system of particles, an external torque changes the angular momentum of a rigid body. To illustrate this very simple concept, we examine a very simply situation. Consider a bicycle wheel. By pedaling the bike we exert a net external torque on the wheel, causing its angular velocity to increase, and thus its angular momentum to follow suit. In the next section , we will use the equation relating torque and angular momentum to derive another conservation law: the conservation of angular momentum....
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This note was uploaded on 02/09/2012 for the course PHY PHY2053 taught by Professor Davidjudd during the Fall '10 term at Broward College.

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