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 .
Newton's second law in angular form for a single particle undergoing linear motion
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 (xpy - ypx) is known as the angular momentum L.
So, the rate of change of angular momentum of a body is equal to the applied torque.
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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 
.
as it passes through
point A in the XY plane. The angular momentum
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 
, we slide the vector 
