How to Find the Torque Required for Gearedmotor?

Put a lever of known length onto one of the hubs and add weights to the end until it moves. Then do the maths arithmetic (havn't I told you this before?)
It works try it.

Calculations are only as good as the figures you put in, the figures were taken as measuremnets. So why not cut out the middle man and measure the actual thing you want in the first place?
Measurement isn't some sort of dirty word...step away from the computer and do some real measurement, it will be more accurate than any calculation wich ignores friction and a host of other factors.

I mean, if you want the length of a steel bar, you don't measure it's cross section, weigh it, look up the density of steel and then calculate it... ? How accurate do you think the result would be?
Del

i think you have all the answers if you would expand you thinking a bit,as much as you are looking for the torque to drive your trolley, have you considered the brake to brake your trolley?

P = 2pi T N/60

F = mass x gravity

T = F R

P = F x V

still actual measurement are more accurate than these denotions.

Small correction here for F, the force

F = friction coefficient X mass X gravity