Cart radical on the left, simplified form of 車. It pictures a cart seen from above with its central axle. An axle is the part the cart turns on, so the radical names the larger object 轴 is a piece of. Same family: 转 turn, 轮 wheel.
Right side 由 supplies the sound - yóu shifted to zhóu in 轴's reading. There's a faint semantic echo (the axle is the rod the wheel runs 'through'), but treat 由 here primarily as the phonetic clue. Same shape sits in 抽 to draw out, 油 oil, 袖 sleeve.
