By David Atkinson
ISBN-10: 158949024X
ISBN-13: 9781589490246
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Additional info for Quantum Field Theory: A Self Contained Course
Example text
38) Thus we obtain the important result that the rate of change of the angular momentum is equal to the moment of the applied force: L = N. 39) It is useful to compare it with the rate of change of the momentum p = F (the quantity L in the rotation motion plays the same role as p in the translational motion, thus the reason to call L an angular momentum is obvious). Since the definition of the vector product depends on the choice of right- or left-handed co-ordinate system, the directions of L and N also depend of this choice.
In any reference , frame (an inertial one) the centre of mass moves with a constant velocity R . and the momentum of the system is p = ∑ m r = MR a α The angular momentum L = ∑(rα × pα ) of a closed system remains constant, because of isotropy of space. The rate of change of the angular momentum of an open system is equal to the torque of the applied forces: L = N. If in a given direction the components of the torque N i = 0 , then the corresponding components of the angular momentum in this direction are also conserved in open systems.
3. , W. D Knight, M. A. Rudermam, Berkeley Physics Course, Vol. 1, Chapter 9. 1 ONE-DIMENSIONAL MOTION One-dimensional motion is motion of a system with one degree of freedom. The general form of the Lagrangian function is already known: L = γ ( q ) q 2 − U ( q ) . 1) transforms into L= mx 2 −U (x) . 2) We could write the corresponding Lagrange's equation, which is of second order. This equation of motion can be integrated in general. But we already know its first constant of motion, expressed by the conservation law mx 2 + U ( x ) = E.
Quantum Field Theory: A Self Contained Course by David Atkinson
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