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I need to size a motor for the following conditions,and I have managed to completely confuse myself:

Motor will turn a hollow cylinder

Cylinder mass = 10000kg

radius = 0.759m

acceleration = 0.25m/sec/sec

Cylinder speed = 19 rpm

I've been calulating the torque by:

T = (I * a) where

I = moment of inertia

a = acceleration

and the horsepower by

HP = (n * T) / 5252 where

n = cylinder RPM

T = torque

I can do all of this fine and the answer come out to around 2hp. However, I am confused about how adding a gearbox to this arrangement will affect the HP needed. I don't see anything in any of these formulas that take into account gear ratio. It seesm to me that if I were to add a significant gear reduction, I should be able to use a much smaller motor.

Where am I going wrong?

Thanks,

Eric