A final dash of physics angular momentum

Consider a particle with mass m moving with velocity v on a circle with radius r. We define a Cartesian coordinate system with the origin at the center and the x- and y-axes in the plane of the circle. See Fig. 1.5A. The magnitude of the angular momentum around the z-axis is given by 

The angular momentum is given a positive sign if the motion of the particle is counterclockwise when viewed down the positive z-axis, and a negative sign if the motion is clockwise. 

The angular momentum may also be regarded as a vector and defined by the vector product 

We now consider a particle that is free to move in the xy plane. See Fig. 1,5B. The angular momentum about the z-axis may be calculated by decomposing the linear momentum vectors in components in the radial and tangential directions  

Note that is equal to zero if the tangential component of p is equal to zero, i.e. if the particle is moving on a straight line through the origin of the coordinate system. 

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