Angular velocity of a particle ↩

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created: 2022-06-24 00:32:51
modified: 2022-06-24 02:32:21

The angular velocity

describes the rate of rotation of a particle with respect to a particular origin. With the implicit definition:

Where is the velocity, is the position and denotes the vector cross product.

Justification

We can take the infinitesimal displacement generated by an infinitesimal rotation the following way:

And divide by to get time derivative:

Since is the rate of rotation: