Consider the following GIF
The bike driver gained relatively large momentum from the ride.
My question is, how the flip he made helped him reducing his momentum and landing safely?
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No doubt if he didn't apply his brakes and made the flip, he'll surely be in an hospital right after. His velocity was ~0 when he started the flip and 100% zero when he's half way through it, so he was only able to harness a little bit of momentum his body had just before the bike stopped to launch himself, and as soon as he's half way, the fall was pretty gentle since the bike has stopped. So all the guy will be giving credit for is the coordination, timing, and precision he put into the stunt.
He converted his horizontal momentum into vertical by a rotation of 90 degrees around his steer. Friction kept the moped into place.
As you say the biker didn't gain momentum for the jump from the motion of the bike in any way. If fact, the bike stopping and the stunt being performed are two separate things. He pushed the seat of the bike with his leg which made him flung into the air(Newton's third law). He landed safely because he had gained expertise with that stunt not because he knew bike riding. Also he braked at the right time and he engaged the bike stand which made performing the stunt much easier for him.