To balance a 40.0-kg automobile tire and wheel, a mechanic must place a 55.0-g lead weight 24.0cm from the center of the wheel. When the wheel is balanced, its center of mass is exactly at the center of the wheel. How far from the center of the wheel was its center of mass before the lead weight was added?
Treat it as a balance beam problem. When the beam is balanced, there's a 55g mass 24cm from the fulcrum. What mass at what distance is required to offset that? We know the mass is 40Kg.
Try it yourself before reading on.
Moment is mass times distance. The moment of the weight is 55g x 25cm, or 1375 g cm (1.375Kg cm). The moment of the unbalanced wheel is therefore 1.375Kg cm which is equal to the mass times distance. Algebra time!