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## Main Question or Discussion Point

In my Classical Dynamics book, I am reading about the topic alluded to in the title of this thread.

Here is an excerpt that is provided me with confusion:

"The total linear momentum [itex]\vec{p}[/itex] of a particle is conserve when the total force on it is zero

Note that this result is derived from the vector equation [itex]\vec{p} = \vec(0}[/itex], and therefore applies for each component of the linear momentum.

The part in bold is particularly confusing. Could someone help, please?

Here is an excerpt that is provided me with confusion:

"The total linear momentum [itex]\vec{p}[/itex] of a particle is conserve when the total force on it is zero

Note that this result is derived from the vector equation [itex]\vec{p} = \vec(0}[/itex], and therefore applies for each component of the linear momentum.

**To state the result in other terms, we let [itex]\vec{s}[/itex] be some constant vector such that [itex]\vec{F} \cdot \vec{s} = \vec{0}[/itex]indepent of time. Then [itex]\vec{p} \cdot {s} = \vec{F} \cdot \vec{s} = \vec{0}[/itex] or, integrating with respect to time [itex]\vec{p} \cdot \vec{s} = c[/itex] which states that the component of linear momentum in the direction in which in the force vanishes is constant in time**The part in bold is particularly confusing. Could someone help, please?