Show equivalence of two versions of angular momentum equations by vector math.

Related BrainMass Solutions

• Express the angular momentum of a marble

  Definition 2: The angular momentum, vector L, of an object about an axis, is defined as the cross product of the position, vector R, relative to the axis, and its linear momentum, vector p.

• Rotational Motion and Angular Momentum

  The reason is that angular momentum L is a vector and is equal to a scalar (moment of inertia) multiplied by a vector (angular velocity). There is nothing that would change the direction of L in this equation.

• Rotational motion: Angular momentum and Torque

  Hence, Magnitude of angular momentum = rpsinθ = p(rsinθ) = Magnitude of the linear momentum x Perpendicular distance of the axis of rotation from the velocity vector Direction of the angular velocity vector is given by the right hand screw rule

• The Energy of Spin-Orbit Coupling

  The orbital angular momentum of the electron is given by: (1.18) So we see that the angular momentum vector is proportional to the magnetic field (remember that the radius is constant) (1.19)   From the point of view of the electron the system

• Angular Momentum and Torque

  Angular momentum of a particle about a point is defined as the moment of the linear momentum vector about the given point i.e. : Magnitude of angular momentum = Magnitude of the linear momentum vector x Perpendicular distance of the line of action

• Collision of particles with symmetry due to interaction.

  The attachment contains the full question which goes on to ask for a description of the symmetry of the configuration. The momentum vector, total energy and angular momentum of the system.

• Equations of motion in a rotatin frame

  these coupled equations, we decouple them by defining: So instead of two second order equations, we get a system of four first order homogenous equations: The characteristic polynomial of the matrix is: So the eigenvalues are

• Commutation Relations of the Angular Momentum Operators

  In other words, we are going to assume that the above equations specify the angular momentum operators in terms of the position and linear momentum operators.

• Spin Angular Monentum

  The principal angular momentum number j which is the eigenvalue of J^2 is a *positive* integer number with sequence difference of 1. Angular momentum is a vector in the calssical sense.