Angular Momentum

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Physics Newtonian Mechanics Angular Momentum

Angular Momentum and Angular Velocity:

Considered a rigid object rotating about the vertical z axis of a coordinate system as shown in the figure.

Now, let us determine the angular momentum of this object. Each particle of this object rotates in the xy plane about the z-axis with an angular speed ω. Then the total angular momentum of the system of particles is given by,

so that the angular momentum in terms of the moment of inertia is

And the total external torque of the system is given by,

Thus, the net external torque acting on a rigid object rotating about a fixed axis equals to the moment of inertia about the rotation axis multiplied by the object’s angular acceleration relative to that axis