The concept of linear momentum 
and the principle of conservation of linear momentum are extremely powerful tools. They allow us to predict the outcome of, say a collision of two cars without knowing the details of the collision. Here, we begin a discussion of angular counterpart of i.e., angular momentum 
.
A particle of mass m with linear momentum 
as it passes through point A in the XY plane. The angular momentum of this particle with respect to the origin O is a vector quantity defined as 
where 
is the position vector of the particle with respect to O. As the particle moves relative to O in the direction of its momentum 
position vector rotates around O. To have angular momentum about O, the particle itself doesn't have to rotate around O.
Angular momentum bears the same relation to linear momentum that torque does to force.
To find the direction of the angular momentum vector 
, we slide the vector until its tail is at the origin. Then we use the right hand rule for vector products, sweeping the fingers from into . The outstretched thumb then shows the direction of in the positive direction of the Z-axis. This positive direction is consistent with the counter-clockwise rotation of the particle's position vector about the Z-axis as the particle continues to move.
To find the magnitude, L = rmv sin f when 'f' is the angle between and .
Sub Topics
Newton's second law in angular form for a single particle undergoing linear motion
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Here, Fx and Fy are two rectangular components of the applied force px and py are the two rectangular components of the momentum p. (at any time t)
But we know,
The quantity (xp
y - yp
x) is known as the angular momentum L.
So, the rate of change of angular momentum of a body is equal to the applied torque.
