In our comparison of linear and angular quantities we suggested that there might be a quantity "angular momentum", (symbol L) equivalent to linear momentum. "Translating" from the linear equation gave us L = Iw.

We might also expect to find a "principle of conservation of angular momentum". Consider the following situations.

A Skater

With arms and leg outstretched (A), the moment of inertia, I_initial, is relatively large. Suppose the skater has a low initial angular velocity w_initial. The skater then gradually decreases her/his moment of inertia by bringing arms and leg nearer to the axis of rotation (B and C). Her/his angular velocity is observed to increase. This is easily explained if we consider that the person’s angular momentum does not change.

If I_initial > I_final then w_final > w_initial

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