Final answer:
When the transfer case shifter catches in neutral, the car remains stationary and may rock back and forth slightly due to the engine's rotational torque. However, the angular momentum of the car is not conserved for long periods of time.
Step-by-step explanation:
When the transfer case shifter catches in neutral, it means that the transmission is not engaged with any of the gears. In an automotive context, the transfer case is responsible for splitting the power from the transmission to the front and rear wheels in a four-wheel drive vehicle.
When the transfer case shifter is in neutral, there is no power being sent to either set of wheels, resulting in the car being stationary. The car may rock in the opposite sense of the engine's rotation because the engine is still generating rotational torque which causes the car to slightly sway back and forth.
However, it is important to note that the angular momentum of the car is not conserved for long periods of time. As soon as the engine is running in neutral, the car starts to lose its angular momentum due to external forces like friction and air resistance.