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__Description of Problem:__I need to buy a motor to drive a custom-made spindle that I have made but I'm not completely sure what wattage the motor needs to be. Basically the spindle is just a hollow cylinder (closed on all sides) of stainless steel attached to the end of a shaft - the shaft will attach to the motor. The cylinder is 0.033m in radius and 0.1m long. The shaft is 0.05m long and has a radius of 0.0035m, so the total length of the spindle+shaft is 0.15m and the total weight of the spindle+shaft is 0.433kg. I need to be able to accelerate the spindle up to a max speed of 3200RPM (335 rad/s).

__My Attempt:__I found online that Power (W) = Torque (Nm) x Angular Velocity (ω, rad/s), so this leads me to believe that once I know the torque required to turn the spindle then this equation should give me the power I need to accelerate my piece up to 335 rad/s. Am I right so far?

So to calculate the torque needed, I found an equation that says -

Torque (Nm) = Radius (m) x Force (N) x Sin(θ)

This is where I got a little confused. What value do I use as the radius? Do I take the full length of the shaft+spindle as the radius (0.15m) or do I take the radius of the hollow cylinder (0.033m)? Also is the Force just equal to the total weight of my shaft+spindle multiplied by gravity? (i.e. 0.433*9.8?)

Any help would be appreciated! If you need more info please ask.