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As many know, when an external force acts on a rigid body and the force's line of action does not pass through the body's center of mass ##c.m.##, the force will cause the body to both translate and

**rotate exactly about the ##c.m.##.**Otherwise, the body will solely translate without rotation.

How is this important result proven? How can we derived this result? I have been looking on several books but none mathematically justify this conclusion...

Thank you!