Dust can be removed out of a blanket using the law of inertia.
Law of Inertia
Law of inertia also called Newton’s first law, postulates in physics that if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by force.
According to the law of inertia, a particle tends to remain at rest or in uniform motion unless acted by an external force. When you jerk the blanket, it moves, but the dust particles remain at their original position. And finally, the dust gets separated. When we beat the blanket with a stick, it comes into motion. But the dust particles continue to be at rest due to inertia and get detached from the blanket.