NASA is going to slam a spacecraft into an asteroid. Things might get chaotic.

Harrison Agrusa, University of Maryland, led the research team that calculated how DART could alter Dimorphos' spin or rotation. This was done by calculating how momentum of impact will affect the asteroids roll and pitch. These results could be quite dramatic. Agrusa says it could begin to tumble and then become chaotic. This was a huge surprise.
Unexpected spinning presents some interesting challenges. This will make landing on the asteroid more difficult. ESA hopes to do so with two small spacecraft as part of its Hera mission. Because of the possibility of an asteroids' path through space being affected by rotation, future attempts to deflect an Earthbound Asteroid could be more difficult.

DART will smash into Dimorphos with an impact similar to three tons TNT exploding and sending thousands of pieces into space. Statler described it as a golf car traveling at 15,000 mph smashing into the sideline of a football stadium. Agrusa and his crew believe that while Dimorphoss' spin will not be affected immediately by the impact, it will cause some changes within days.

Dimorphos will begin to wobble slowly very soon. As the momentum of the impact causes Dimorphos to spin out of balance, the wobble will only get worse. There is no friction in the vacuum of time to slow it down. Dimorphos might start to spin in one direction or another. It could begin to spin along its long axis like a rotisserie. Didymos observers will notice a change in the satellite's appearance. It will begin to swing back and forth, revealing previously undiscovered sides.

Dimorphos can spin so fast that it becomes uncontrollable around its axes within weeks. Agrusa says that in extreme cases, the tidal lock may break with Didymos and Dimorphos could start flipping over its axes.

There are a few factors that will determine what happens. It will be affected by dimorphosis shape. If it is more elongated than spherical, it will spin more chaotically. Its radar observations suggest that it is elongated. However, we will not know this until DART hits and it sees its small target for the first time.