Washer won't spin fast in the spin cycle to wring clothes

My washer won’t spin during the spin cycle in Colors. When is switch over to whites and try to rinse the drum spins but not as fast as it used to leaving the clothes soaked when the wash cycle is done. I did some research and saw that a lot of spin problems occur from the thrust bearing kit. I just want to confirm that is the problem before I make the purchase. I tipped my washer over, removed the belt, and turned the large white pulley. Turning it one direction spins the agitator. Spinning it the opposite direction moves the drum. Could this be the transmission or the thrust assembly kit?