Answer
See explanation.
Work Step by Step
A tail rotor is necessary for helicopters with one main rotor to prevent the cabin from spinning when the main rotor changes speed.
When the helicopter is airborne and moving at constant velocity, no net external force acts on it, and no net external torque does either. Its angular momentum is conserved. If its main rotor were to, say, increase in speed, then to balance out this increase in angular momentum, the passenger cabin would have to rotate in the opposite sense as the main rotor. This can be prevented by having a tail rotor that applies thrust sideways, causing a net torque upward or downward.
Some helicopters, such as the Chinook, have two main rotors that rotate in opposite senses (one clockwise, and one counterclockwise as seen from the top). The net angular momentum of these rotors is zero. If they both increase in speed, or both decrease in speed, because they are rotating in opposite directions, there will be no net change in angular momentum, and the main cabin does not tend to begin rotating. No tail rotor is necessary.
