Angular Momentum

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Physics Newtonian Mechanics Angular Momentum

Conservation of Angular Momentum:

The conservation of angular momentum states that the total angular momentum of a system is constant in both magnitude and direction if the resultant external torque acting on the system is zero. That is, for:

L = constant. And for a system of particles this law is given by,

where n is for the nth particle of the system. In terms of angular velocity and moment of inertia the conservation law is given by,

The Spinning Top : The motion of a top has been shown in the figure. The precessional motion of the top is usually slow relative to the spin motion of the top. Since, the center of mass is not directly above the pivot point O, a net toque is acting on the top about O due to the weight Mg. The angular momentum L is directed along its symmetry axis. This type of motion is an excellent example of the importance of directional nature of angular momentum.

There are two forces acting in the downward direction:
the force of gravity and the normal force n acting upward at
the pivot point O. The normal force does not produce a
torque. However, the force of gravity produces a torque
given by,