I got a Nikon 3400 in May. While shooting some water droplets I noticed the droplets contain motion blur even at the highest shutter speed settings. So I tried to verify this by clicking a pic of the ceiling fan [In India]. I might not know the exact speed of the fan, but I am sure as hell the fan does not do more than 4000 rotations per second. And yet, I get motion blur on the fan. Images attached.
Is my camera broken? Should I get it repaired? Or am I not understanding something?
Shutter Speed: 1/4000 sec
ISO : 25600 (It was indoor)
Update: The problem does not occur when I click the image in Live View Mode. The image appears darker and the motion is frozen. But When I switch to View Finder mode, something's not right.
Added Settings Images.
PS: I checked the image properties and all the settings and details are exactly same. The camera does not show any change in the shutter speed value it displays.
Update: Check out the experiment at http://atulbhats.com/cam-demo