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Unformatted text preview: Angular Momentum: a summary Here are some of the important relations involving angular momentum. The basic relation, for a point mass = mr v which becomes = mrv = mr 2 or = z = mr 2 z = mr 2 which defines the vector . For many masses, we write L = X i i where all the separate i are calculated with respect to the same axis. This can be written as L = X i m i r 2 i or L = I which defines the Moment of Inertia as I = X i m i r 2 i The rate of change with time of angular momentum is caused by torques. This is a consequence of Newtons 2nd Law, F = ma , which can also be written as F = mdv/dt = dp/dt where p is the momentum. The important relations are For one point mass G = r F = mr dv/dt or (see the textbook, or your notes from class) G = md [ r v ] /dt = d /dt For a rigid body (a collection of point masses which are rigidly attached to each other) G ext = X i d i /dt = dL/dt 1 which can also be written as G ext = Id/dt for motion around a fixed axis. The torquefor motion around a fixed axis....
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