Well, this is mostly guessing, but: the inertia would only make the bucket accelerate slower. It would not increase or decrease the weight needed to set the bucket off. This is of course if we start with a stopped motor, to test the holding torque, as Jeff suggested (and to which I agree).
The end-connected rod: the mass centre of the rod is in its middle (assuming it's a uniform rod that doesn't get thicker in one end, for example). So the torque exerted by the rod equals its weight times half its length (assuming now that it's horizontal). Since you multiply the final weight with the full length of the rod, you must add only half its weight to the final weight - this is the same as first calculating the torque produced by the bucket, and add that to the torque of the rod. With M = total torque, Fb = force-bucket, Fr = force-rod, Lr = length-rod:
M = Fr*Lr/2 + Fb*Lr = (Fr/2 + Fb)*Lr
I agree it would be a good idea to give the bucket a push - but we want to see if the motor is able to stop the motion, not sustain it (it's the HOLDING torque we are after). Still, any moment of intertia of the spool would only delay the braking a bit, and not affect the motor's ability to actually hold the bucket or not.
Arvid  |