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.
Let pr and pq be the radial and angular components of linear momentum respectively . The radial component pr will not contribute anything to L. The only effective component is pq.
Here, we see some similarity between angular momentum and torque. Both of them depend on the location of the particle in a similar way. If torque is the measure of the turning effect of the force, angular momentum is a measure of the turning movement of the object.
