# How to determine the right spec of a servo motor given an inertia moment?

I'm working on a trash bin which lid is controlled (opened/closed) by a microcontroller and thus i decided to use a servo motor.

The lid is 47 x 47 x 0.1 cm and because its made from steel has a density of 7.874 g/cm^3. Assuming uniformity, this means that this lid has an inertia moment of 0.096057 kg.m^2 with the axis being on the bottom-middle of the lid. I want the servo to be able to open the lid 60 degree in 2 seconds for convenience reasons.

When choosing from a variety of servo motors, i noticed that they write torque not in Nm but in Kg/cm which makes no sense to me. I just gave it a shot and use a 17 kg/cm servo and placed it in the middle of the lid but apparently its not strong enough. So how to properly calculate the right spec of a servo motor given this application ? Thank you so much beforehand i'm still new to this

• I'm voting to close this question as off-topic because this is mechanics, try the physics stack Mar 1, 2020 at 12:42
• The question revolves around servo spec selection so i thought this belongs here Mar 1, 2020 at 12:44
• kg/cm is not correct for torque, but quite a common error. Normally, manufacturers specify a motor on the mass it can lift (on Earth!) at a given radius, so 1 kg cm = 9.81 N cm = 0.0981 N m
– Chu
Mar 1, 2020 at 12:54
• Inertia may not be the only consideration, unless the lid is perfectly balanced (and who balances the lid on a trash can?)
– user16324
Mar 1, 2020 at 13:40

Inertia doesn't matter very much given the way this is set up. (Side note, it's $$\kg\ cm\$$ not $$\kg/cm\$$, and it's really kg on earth, so it works out as a unit of torque, albeit a silly one). You know the mass of the lid, work out the length of the lever arm being applied to the lid to lift it. Convert the mass to kg, lever arm length to cm, multiply them together, give yourself some safety factor (~20%), buy a servo with that $$\kg \ cm\$$ rating or higher.