Can I make an electric motor spin faster by increasing the voltage?
Increasing voltage will not work… you need to increase current. An electric motor is based upon current producing a force against a magnet. The speed is not based upon voltage. You can make it faster by using less resistance… to do this without changing your power source you will have to use lower resistance wires (made of better metals, shorter, and thicker). Soldering the connections will also help as it forms a solid connection rather than a rough, temporary connection. If you have a switch in your circuit, remove it and use a simple wire movement. Switches have a lot of resistance.
