Motor torque calculations

I am designing a kinetic display for a client and I need someone to do the math on how much torque is required to make each one of these modules spin. I have a nema 17 motor thats driving a ring gear. The ring gear is going to be approximatly 200 teeth and nema 17 motor will have a 30 tooth gear or close to. So the gear reduction on that will be around 6:1. But I need to figure out how much my motor will need to output to make this move. You will see in the model that the motor is fixed and 2 injection molded ABS clamshells come together with Delrin (Acetal) riding surfaces. If someone can do the calculations to figure out the torque in Nm that will be necessary that will help me spec out the appropriate motor. The arms that hangout will be aluminum tube and the pucks on the end will be acrylic.