It's easy to create a motor that can spin up to ten thousand revolutions per minute powered by a single battery. All it takes is a battery, a wire, a screw, and a circular magnet. You can build a tiny homopolar motor within a minute.
Most motors are tough to build. This is because they're meant not only to provide mechanical power, but to provide mechanical power to a specific machine with specific needs. They have to fit into the machine and move powerfully and quickly enough to be useful, but not quickly and powerfully enough to tear it apart. Such is the price of practicality. If you want to dispense with all of that and just see something spin at a huge speed, you can make the motor that Michael Faraday made back in 1821. It was the first electric motor ever built, and it can be built (now) in less than a minute.
It requires a battery, a screw, a disk magnet - which must all be lined up - and a piece of wire long enough to connect them all. Grab the disk magnet and put it on the flat end of the screw. The magnet has to be powerful enough that the screw will be magnetized and cling, by its pointed tip, to the negative end of the battery. Now attach the wire to the positive end of the magnet and bring the other end of the wire close to the magnet. The screw should begin to spin.
Why? Well, it has to do with the interaction of the magnetic field with the electric current. One flat side of the disk magnet is its north pole and one is its south. Anyone who's seen a diagram of the magnetic field lines of a magnet knows that they go north-south. If the magnet is hanging down from the battery in front of you, the magnetic field lines would roughly form the vertical line of a plus sign. The electric current moves through the magnet from the edge to the middle. Again, looking at the magnet hanging down, the electricity is flowing along the horizontal line of the plus sign. When electrons move this way through a field, they experience a push that is at right angles to both the field and their motion to it. Since the 'plus sign' has already taken all the right angles in two dimensions, the push they're experiencing has to be a line coming 'out' of the plus sign, towards you. (And away from you.) That's the direction of the force pushing them. This causes the magnet to get pushed forward (or back) making it spin.
There are a lot of ways to make this motor, all with magnets, wires, and batteries. This is the easiest way, and it creates one of the fastest motors. Since the only point of contact the moving screw has is with the edge of the wire and the place where its tip touches the battery, the entire motor experiences very little friction. This means it speeds incredibly fast. Depending on the battery or the wire, it can revolve thousands of times per minute. It's an incredibly fast mover. It just can't 'do' anything.
Top Image: UAB