Although these aren't quite like the spinning tea cups in Mad Tea Party in which you can control your spinning, the Alien Swirling Saucers move around in circles and sway side to side (the more weight in the cart, the more it'll sway). If your child isn't a fan of spinning or gets car sick easily but wants to try it, watch people ride it from afar a few times, and you'll get a pretty good idea of speed and how much it spins.
If you think they'll be OK, but you are still a bit concerned about the spinning, rather than pack two adults and one child into the cart, try one adult and one child so there's less weight and less swaying back and forth as you twirl your way through the ride (or, if they're big enough, let them ride alone so there's even less weight).
Image Source: POPSUGAR Photography / Alessia Santoro