When a car turns, the outside driven wheel travels a longer arc than the inside wheel, so it must rotate faster. A differential lets the two axle shafts turn at different speeds while both are driven by one input.

For a simple symmetric open differential, wheel speeds satisfy

where ω꜀ is the differential-carrier speed. If both wheels turn equally fast, each matches the carrier. If one slows in a turn, the other speeds up correspondingly.

The clever mechanism is the spider/side gears: during straight-line driving they can rotate together as a locked-looking assembly; when wheel resistance/speed demands differ, the spider gears rotate on their own axes and permit relative axle motion.

The open-differential catch: an open differential delivers essentially equal axle torque to both sides, so usable drive can be limited by the wheel with the least traction. If one wheel can support only a small torque on ice, the other wheel does not automatically get all the spare engine torque.

Limited-slip differentials add friction, clutches, gears, or other mechanisms to bias torque toward the wheel that can use it. A locking differential goes farther and forces the axle speeds together when locked.