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Dear student,
Consider a particle capable of rotation about an axis. At any time t, let its momentum be and , the position vector. Then the angular momentum is given by the cross product and . = x .
In three dimensions,
Lx = ypz - zpy, Ly = zpx - xpz, Lz = xpy - ypx.
The angular momentum, which is nothing but moment of linear momentum, can be expressed in terms of the lever arm for momentum.
Let us consider the case of angular momentum in two dimensions.
L = xpy - ypx
If j is the angle between and x-axis, then px = p cos y and py = p sin y. Also x = r cos q, y = r sin q.
Hence, we can define angular momentum as the product of linear momentum and the lever arm for momentum.
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