Detachment (noun)

1. The state of being detached.
2. The act of separating something from something else.
3. A detachment of troops or police.
4. The ability to remain emotionally removed from a situation.

Origin:

Late 16th century: from french détachement, from détacher "detach".

Examples:

1. The detachment of a muscle from its bone.
2. The detachment of a satellite from its rocket.
3. The detachment of a colony from its mother country.
4. He approached the problem with a detachment that was almost clinical.
5. His detachment allowed him to make an objective decision.