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Unformatted text preview: Physics 225/315 February 8, 2008 Classical Angular Momentum and Torque A rotating vector A is a vector with fixed magnitude in three dimensional space. It makes an angle with the z axis. A rotates around the z axis through an angle . The angle is in the x, y plane. A = A sin A = A sin t t dA d = A sin dt dt dA =A dt since the angular velocity = The direction of
dA dt d . dt is along the axis of rotation. is perpendicular to A and perpendicular to the axis of rotation. A Asin Torque and force The torque = r F Angular momentum L = r p dp dL =r =rF = dt dt p = 0 since velocity is in same direction as momentum, p. where we have used dr dt 1 Magnetic Moments The torque on a magnetic moment, M , in a magnetic field, B, is =M B The magnetic moment is related to the spin angular momentum M = S. where is the gyromagnetic ratio. Since
dA dt =A and = = dL dt dS 1 dM = = M B = -B M = S B dt dt or dS = -B M dt dM = - B M dt Use
dM dt = M then the precession angular frequency is = - B 2 ...
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