# Contradictory units for moments of inertia

I'm looking at a motor datasheet where the moment of inertia is specified in units of "oz in sec^2". I would think that inertia should have dimensions of mass * length^2.

I did some further Googling and found that some automatic unit conversion calculators (example) let you convert between seemingly contradictory units - the site I've linked lists both kg-m^2 to kg-m-s^2 as acceptable units for moments of inertia. What am I missing here?

I spent some time searching on this one, and surprise surprise, Imperial units strike again!

The good old "pounds-force pounds-mass issue" masked with ounces. This is why any calculation more involved than sizing a pulley should be done in metric, lol.

Oriental Motor- Basics of motor control, explains the following:

Units of Measure for Moment Inertia

The units of inertia are commonly used in two ways, oz-in2 and oz-in-sec2. The former includes gravity, the latter only mass.

Theoretically, inertia is factor of mass so it should not include gravity, however, practically we can not easily measure mass on the earth.

Oriental Motor commonly provides inertia in oz-in2. Then, when we calculate the Acceleration Torque in Torque Calculation we divide the total the total inertia by the gravity from.

Gravity = 386 in/sec2

• oz-in2 = Inertia based on weight
• oz-in-sec2 = inertia based on mass

Calculation for oz-in2 to oz-in-sec2 So an oz-in-sec2 does exist because it's an ounce-force not an ounce-mass.

A kg-m-s2 does not exist, because kg is mass not force. You could convert oz-in-sec2 with Newtons, but I wouldn't even go there, lol.

The best course of action is to follow Oriental Motor's guide to get to oz-in2. Then convert to metric kg-m2 and don't look back ;-)