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If it's not moving, the force of gravity acts on it,
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causes an acceleration toward the center.
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That means what you and I think it means, falling toward the center.
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But if you take an apple with a huge velocity to begin with,
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add to it an acceleration toward the center,
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or a tiny increment of velocity in this direction--
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we will just give it that velocity--
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and that's the velocity it has when it has come here
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Same thing with the gyro.
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The gyro does get the same angular momentum ΔL that it would
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whether or not it was rotating
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But in one case, you add it to zero