What could cause a gear to be seized to its shaft?

A gear can become seized to its shaft due to several factors, and excessive spinning of the tires when stuck in mud is particularly relevant. When tires spin rapidly while stuck, it can create significant heat and stress in the drivetrain, which may lead to the expansion of the components. This thermal expansion can cause the gear to become jammed on its shaft, especially if both the gear and shaft are made of materials with different thermal expansion rates or if there is inadequate lubrication to dissipate heat.

Additionally, while the use of synthetic oil generally provides better lubrication properties and high thermal stability, using it does not inherently cause gears to seize. In fact, synthetic oils can help prevent seizing by maintaining proper lubrication under high-stress conditions. Driving at high speeds does not typically result in gears seizing unless there are underlying issues, such as insufficient lubrication or pre-existing damage.

Therefore, the action of spinning the tires excessively in mud creates an environment where heat and friction can lead to a gear seizing on its shaft, making it the most applicable cause in this scenario.