How do you tweet a partial YouTube video?

I know I can share the video by copying the url and pasting it into the tweet but how do I tweet those 30 second videos of a specific part of the video? I see everyone doing it but I haven't figured it out. I have been searching google and it only tells me how to embed the full video from youtube.
Sorry I'm new to twitter so I have no idea!

Updates:
Rewarding MO to anyone that helps me.

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