Unbalanced Forces
Unbalanced forces do not cancel out; they produce a nonzero net force that changes an object's speed or direction.
Definition
Unbalanced forces are forces that do not cancel out: one side wins, so the object starts moving, stops, speeds up, slows down, or turns. Forces are unbalanced when the net force is not zero, and the object accelerates in the direction of that net force, changing its speed, its direction, or both, with a larger net force giving more acceleration for a given mass. In symbols, $\vec{F}_{\text{net}} \neq 0$ and by Newton's second law $\vec{a} = \vec{F}_{\text{net}}/m$. The net force may be unbalanced along one axis while balanced along another, which is the situation for an object sliding on a horizontal floor: vertical forces cancel, horizontal forces do not. Uniform circular motion is a case of a perpetually unbalanced force with constant magnitude.
Example
In a tug-of-war where one team pulls harder, the rope moves toward the stronger team because the forces are unbalanced. A $60\ \text{kg}$ swimmer who pushes off the wall with $240\ \text{N}$ against $60\ \text{N}$ of water drag feels a net force of $180\ \text{N}$ and accelerates at $180 \div 60 = 3\ \text{m/s}^2$. In circular motion, a $0.50\ \text{kg}$ ball on a $2.0\ \text{m}$ string moving in a horizontal circle at $4.0\ \text{m/s}$ needs an unbalanced centripetal force of $F = mv^2/r = 0.50 \times 16/2.0 = 4.0\ \text{N}$, supplied by string tension and always pointed toward the center.
Key Insight
Any time you see something change its motion, unbalanced forces are at work; a rolling ball slowing to a stop is being acted on by an unbalanced friction force. Unbalanced forces are needed to change motion, not to keep it going, so once the swimmer is gliding, only friction, an unbalanced force backward, slows her down. The direction of the net force is the direction of acceleration, not necessarily the direction of motion. A ball thrown upward moves up while the unbalanced force of gravity points down.