Why do electric motors have different shapes and sizes?

Alright, imagine you're designing a motor. You need to consider the power requirement, speed, torque, and where it's gonna be used. For example, a motor for an electric car needs to be compact and powerful, while a motor for an industrial fan needs to be efficient and durable. The shape and size change based on these needs. Plus, the design affects how much heat it generates and how it cools down. It's all about optimization, my friend! Also, the math behind it is pretty cool. The power of a motor is given by $$P = \tau \omega$$, where $$\tau$$ is torque and $$\omega$$ is angular velocity. So, depending on what you need, you'd design the motor differently.