Question

Under what conditions is the momentum of a system constant? Can the $\mathbf{x}$ component of momentum be constant even if the $\mathbf{y}$ component is changing? In what circumstances? Give an example of such behavior.

Short answer

The momentum of a system is constant if there is no net vector force on the system.

Yes,the $x$component of momentum be constant even if the$y$ component is changing if the object is moving in $xz$ plane.

Step-by-step solution

Significance of the momentum of a system

Momentum is defined as the product of the mass and velocity of the object and it can be changed by applying the force to the object. So, it can be constant if no external force acts on the system.

Identification of the condition of the constant momentum of a system

In the case when net vector forces are not acting on the system, then the momentum is said to be constant.

Assume that a ball is moving in $xz$ plane. In this condition, gravitational force and centripetal force will act in $y$ direction only that will result in the change in the $y$ component of the momentum. There will not be any force that will act in $x$ direction , so there is no change in the $x$ component of the momentum.