Circular Motion in a Fixed Plane

Rgure 5.2 The right-hand screw rule for determining the direction of the angular velocity or angular momentum vector 

Because 0 = sir and d /df = v, it is possible to write the following expression for the magnitude of the angular velocity. 

The kinetic energy of the particle is constant, and equal to m H. In terms of the angular velocity m, this can be expressed as  

The quantity mr- is known as the moment of inertia of the particle and is given the symbol /. Thus  

This equation has the same form as the equation for linear motion, but with moment of inertia and angular velocity substituted for mass and linear velocity, respectively. For rotational motion it is generally true that the angular velocity and the moment of inertia have an analogous role to velocity and mass in linear motion. In keeping with this principle, we can define an angular momentum vector, L, as follows  

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Q For circular motion in a fixed plane, show that the Laplacian operator given in equations (5.22) and (5.23) leads to the Schrodinger equation derived in Section 5.1.2. 

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