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In mathematics a differential is the expression which appears inside an integral in calculus. It is less meaningful outside an integral, but can be thought of as representing a very small change.
In an automobile and other wheeled vehicles, a differential is a device for supplying equal torque to the driving wheels, even as they rotate at different speeds.

In some vehicles such as karts[?], torque is simply applied evenly to all driving wheels using a simple driveshaft. This works well enough when travelling in a straight line, but when changing direction the outer wheel actually needs to travel further than the inner wheel. Hence, the simple solution results in the inner wheel spinning. For general road use, such a method would result in too much damage to both the tyre and road surface.

Explain how a differential works here, but it's *very* difficult to show without animation...

A four-wheel-drive vehicle will have at least two differentials (one for each pair of wheels) and possibly a centre differential to apportion torque between the front and rear wheels. Vehicles without a centre differential should not be driven on dry bitumen roads in four wheel drive.

The standard "open" differential is not ideal for vehicles driven in conditions where wheelspin is common. In these conditions (which can include muddy or snowy conditions, or when the vehicle is driven particularly vigorously) it is advantageous to direct more torque to the wheel that is spinning slower. Various types of limited-slip differential have been invented for the purpose.

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