Question

Why do dust particles start coming out of ahanging blanket when it is struk with a stick?

Answer 1

because of the inertia of rest, when a blanket is struck with a stick the blanket starts to move but the dust tries to remain in its position and so it comes out of the blanket.

Answer 2

It's because of a physics, the inertia. The carpet is a cloth and dust sticks to it very easily. When you hit the carpet a sudden deformation is faced by carpet's surface, because of the force with which it has been strucked, so the dust particles stays at the same place which allows them to leave the carpet's surface and the disturbance in the air by the stick gives motion to these dust particles in the air which our eyes witness as a turbulence. 

Be it a stick or your hand (try the same thing with your pillow or sofa set you have at you place) you'll get the same result.