Final answer:
The side gears in a differential are connected to the wheels and rotate with them, while the pinion gears allow the side gears to turn at different speeds, which is essential during a vehicle's turning and cornering.
Step-by-step explanation:
Within the context of a vehicle's differential, the side gears and the pinion gears work together to allow the wheels to rotate at different speeds, particularly during turns. The side gears are connected to the axle shafts and therefore, are directly linked to the wheels. When a vehicle turns, the outer wheel needs to rotate faster than the inner wheel to maintain traction without slipping. The pinions, which mesh with the side gears, are mounted on a cross-pin and can rotate freely. They provide the mechanism that allows the side gears to rotate at different speeds. So, the side gears are directly affected by the motion of the vehicle's wheels, while the pinion gears serve as intermediaries that allow the side gears (and hence the wheels) to turn at different rates when necessary. This differential action is key to providing smooth turns and maintaining stability and traction of the vehicle during cornering.