What is the name of the technique that gives the sensation of rapidly moving objects in a still image? How to reproduce that?
Is it possible to reproduce it with a smart-phone camera and an free App? Or just professional cameras?
This effect is a simple motion blur. You recreate it with using a slow shutter, low ISO, low light and a steady hand or a tripod. The person just moves the body part.
Try this simulator out. On the running dog image, check "Link" then move the shutter slide to the left. Longer exposure makes moving objects blurred.
To recreate this on your smartphone, you need to either manually control shutter speed, aperture and ISO (most newer smartphones allow that) or create a sufficiently dark environment so that the camera cannot compensate against it with ISO and aperture.
You basically want the shutter to be open while the head is moving. You can try 1/15 or so (depends on the speed of movement). Long shutter means you have to reduce the amount of light coming in the camera. You do that by decreasing aperture (larger f/number), decreasing ISO, decreasing external light, in any combination.
You need the camera be steady while photographing, otherwise you introduce another blur: camera shake blur ;-). This case the background will be blurred as well.
How to reproduce that? On a retouching software you go to... Effects > Motion blur... Normally you need to work in a specific layer.
If you are refering to a photo you simply use a slow shutter speed. How low? depends on how fast the object is moving, how close you are to that subject so what is the relative distance you need on the framing to be covered.
It is usefull to use a tripod so the only thing moving is the subject and not all the image.
If you are the one moving, is usefull to fix the camera to a reference, for example a helmet of a biker.
On an automated camera like a phone, try taking the picture on a low light situation. That is the only thing you can do. You could try to use ND filters. No need for a free app.