Step 1: Recall Newton's first law. An object remains at rest unless acted upon by an external force (law of inertia).
Step 2: Application. When the blanket is beaten, the blanket moves but the dust particles tend to remain at rest due to inertia, so they get separated.
Step 3: Conclude. This is a clear example of Newton's first law of motion.
\[
\boxed{\text{Newton's First Law of Motion}}
\]