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Does a spinning, non-translating rigid disk have linear momentum as well as angular momentum (constraining it to have constant angular velocity)? I believe it doesn't have linear momentum since there is another asymmetrically-moving infinitesimal mass element for every infinitesimal mass element. I just wanted to make sure.

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    $\begingroup$ You can show that if the center of mass is not moving then P=0 $\endgroup$
    – user65081
    Commented Jun 27, 2021 at 15:21

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By circle I assume you mean a hoop, and by spinning I assume you mean it is rotating around its axis of symmetry.

Then for every mass element along the circumference of the hoop in a direction x there is another mass element on the opposite side of the hoop moving in direction -x, so any linear momentum gets cancelled.

As Wolfram jonny points out, if the center of mass of the hoop is stationary, then its linear momentum will be zero. This is the easy way to answer the question if you don't mind doing the math.

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