# Need help picking motor to wind a spool

The application is a motor attached to a spool to wind/unwind window blinds. I would like to operate the motor at $$v=0.2\text{ m/s}$$, with a max load of 1.5 kg.

I need to know the ideal diameter of the spool and the specs for the motor! It seems I need to use a static value for spool diameter to determine specs so if I use $$d = 1\text{ in} \approx .025\text{ m}$$:

• Force (constant) $$= mg = 1.5 \cdot 9.81 = 14.72\text{ N}$$
• Torque (constant) $$= Fr = 14.72 \cdot 0.025 = 0.37\text{ Nm}$$
• Power (constant) $$= Fv = 14.72 \cdot 0.2 = 2.94\text{ W}$$

I'm pretty sure that not accounting for instantaneous requirements due to initial acceleration, these specs are appropriate. But what about the angular velocity of the motor? This is where I'm getting hung up.

required angular velocity of spool $$w = \dfrac{\text{linear velocity}}{\text{circumference of spool}}$$

$$w = \dfrac{v}{c} = \dfrac{0.2}{\pi \cdot 0.025} = 2.55\text{ rad/s} = 152.7\text{ RPM}$$

So this is not the required rpm of the motor? Do I have to account for the radius of the output shaft of the motor to calculate the required motor speed?

So far I was thinking this would work but like I stated I'm not sure if the output w = input w.

Also are the specs provided for gear motors are the output including the gear ratio, or do I need to multiply the spec by the gear ratio to find actual output?