Challenges:
* Power Conversion: A 12V motor can't directly power a 12V alternator effectively. You would need a mechanism to increase the speed of the motor to spin the alternator at a sufficiently high RPM to generate enough power.
* Efficiency: The conversion process of motor to alternator to battery charging would be very inefficient, losing significant amounts of power along the way. This means your 12V motor would need to be quite powerful to deliver a usable charge to the battery.
* Size and Weight: A powerful enough motor and the necessary gearing would be bulky and heavy, making it impractical for a car stereo setup.
* Regulation: Charging a battery requires careful voltage and current regulation. You'd need a sophisticated system to manage this, adding to the complexity.
Better Alternatives:
* Direct Battery Power: The most straightforward solution is to directly power the car stereo from the car's battery.
* Solar Panel: A small solar panel could charge the battery, especially if you park in a sunny location.
* Portable Power Bank: A portable power bank with a USB output can power the stereo for a limited time.
* Generator: A small portable generator could charge the battery if you need a continuous power source.
In summary: While the idea of using a 12V motor to charge a battery for a car stereo is intriguing, the technical hurdles and inefficiency make it impractical. Consider simpler, more efficient alternatives.