Momentum for a system can be conserved in one direction while not being conserved in another. What is the angle between the directions? Givean example.

The product of a particle's mass and velocity is called momentum. The term "momentum" refers to a quantity that has both a magnitude and a direction. The temporal rate of change in momentum is equal to the force applied on the particle, according to Isaac Newton's second law of motion.

The momentum of an object, $p=mv$, is a vector quantity. That is it has both magnitude and direction.

In the vector form, we can write the momentum as,$\overrightarrow{p}=m\overrightarrow{v}$

A vector can be resolved into two components, one is along the x-direction and the other is along the y-direction. The below figure represents the vector diagram of $\overrightarrow{p}$

where$\overrightarrow{p}=p_y\sin \theta$is the y-component of the$\overrightarrow{p}$ along the y-direction and$\overrightarrow{p}=p_x\sin \theta$ is the x-component of$\overrightarrow{p}$ along y-direction. Where $p_x$and $p_y$ are the magnitudes of $\overrightarrow{p}$ along the x and y-direction.

If the net external force acts along anyone of these x and y-directions is zero, then the momentum is conserved along only that direction. Thus the angle between these directions must be 90° as shown in the diagram given above.

One example of conservation of momentum is during projectile motion, if the air resistance is negligible; momentum is conserved in the horizontal(x-direction) direction because net horizontal forces acting along this direction is zero.