It's very possible to spin something fast enough to create a sonic boom, but engineers usually try very hard to avoid it.
Several aircraft have been built, on purpose, with supersonic propellers. One production aircraft is the Tupolev TU-95 Bear long-range bomber. Eight counter-rotating 4-blade props turn fast enough so the prop tips are supersonic. Rumour has it that the plane is loud enough to be heard by submarines - be happy you don't live near one of their bases.
Another is the XF-84H Thunderscreech, an experiment back in the 1950s. The prop tips moved at Mach 1.1 even on the ground, it was apparently audible 25 miles away and the shock wave from the prop tips was not only dangerous to the ground crew but actually visible far from the aircraft.
Note that you don't get a boom in either case, you get a constant very very loud noise.
So, if you want to break out your Dyson's motor and extend the rotor a bit it could very well go supersonic. Highly unlikely the motor has enough power, and you will need to balance the shaft very, very carefully. Wear earplugs! (and maybe body armour)