Here's the easiest setup with the lowest learning curve I can think of. What you can do is you can buy this robot car kit for $36: https://www.amazon.com/dp/B0794PWD7J/ref=psdc_2528074011_t1_B07KPZ8RSZ
I am not affiliate with this seller in any way.
Then you just need to glue/double-sided tape the bottom of the lazy susan setup to the top of a car wheel and figure out a way to hide the car setup in your video.
You can modify the speed of the wheel by adjusting the sleep time and toggling the motor voltage from low to high in code. When a motor voltage is low, the wheel will not move. When it's high, it will move at max speed. In order to slow down the motor, you can sleep for a fraction of second, then move for a fraction of a second, then sleep again. The car kit will come with a manual to help you understand.
So now the more complex answer requiring more technical know-how:
- You will need a DC motor. A motor has a metal rod at the end so you need a shaft attachment so you can glue the lazy susan to the top of it. Make sure the DC motor has enough torque to spin your lazy susan and whatever is on it.
You can control the DC motor with a circuit controlled by an NE555 timer chip. You can google NE555 timer DC motor setups and you'll get some circuit diagrams which you will have to build. Alternatively, you can buy and arduino/microprocessor to control your DC motor.
You can use a servo motor as well such as the MG996R. Servo motors comes with servo horns which you can glue/double-sided tape the lazy susan directly to. You modify the servo motor to be able to spin continuously. Here's all the info you'll need if you go down that route: https://www.youtube.com/watch?v=J8atdmEqZsc