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# Rotation Inertia

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## Rotation Inertia

(OP)
I have come across two units for rotational inertia, Wr2 and Gd2. both have the same units of measure, could someone clarify which one should I use to calculate the accellartation time of machine rotor. accellerating torque is known.
Replies continue below

### RE: Rotation Inertia

The inertia must be in "Mass Units."  Just as

Force = Mass x Acceleration

Torque = Mass Inertia x Angular Acceleration

If you come up with an inertia based on Weight x Distance^2, divide by one G units, i.e., 32.2 ft/sec^2.

### RE: Rotation Inertia

It is a lot clearer in SI units!!!

Inertia units are only:  kg(kilograms) x m^2 (metres squared)

kilogrammes are a MASS, not a weight (so inertia doesnt care whether its on Mars or some distant star (not sure about black holes though!!)

The problem with Imperial units is that lbs are a weight and thus has gravity embedded in the unit so you have to divide by gravity to get rid of it.  The problem then is, you end up with units of sec^2 on the top of the inertia value meaning that inertia increases with time!!! - that is defintely not the case.
Hope this helps!

### RE: Rotation Inertia

solider,

I have no problems using English _and_ metric units.

Pounds are weight.  Kilograms are mass.

m = w/g.

I always wind up with rotation inertia units in mass format, although the units look a little ugly in English.  I hate using slugs.

JHG

### RE: Rotation Inertia

Hi drawoh,
I suppose inertia should be called "second moment of mass".  (kg*m*m) That is
kg(mass) * metres (first moment) * metres (second moment!).

In the same way "second moment of area" is written as meters^4, but could be written as m^2*m^2. That is:
m^2(area) * m (first moment) * m (second moement).

In the end, I have no problem with either units, either.  The only thing is, if I start in lbs, slugs or whatever, I convert all the units in to metric first, using appropriate factors, and then work out the problem in metric.  Finally, I convert the "result" back to imperial using the appropriate factors, if my customer wants it in English, that is.  That goes for ANY mechanical calculation, not just inertia.  It's, just that I work much more efficinetly in metric, becuase I know exactly where I am.

Then again, I am from the UK.

### RE: Rotation Inertia

solider,

I feel comfortable working in either system of units.  I work in whichever set of units most of my data is in.  If I am using English units and I encounter a mass term in an equation, I substitute w/g.

I do a unit balance when I am done.  I had a mechanics of machines instructor in college who insisted on this, and he has kept me out of much trouble.  His idea probably was that kg.m/s is not a proper unit for acceleration, but it is also helpful around around multiple systems of measurement.

JHG

### RE: Rotation Inertia

drawoh,
Now you have me confused!

kg.m/s is definitely NOT a unit of acceleration. The only metric unit of linear acceleration, if we are taking about metres, is m/s^2.   There is no "probably" about it.  Or are you saying it "tongue in cheek" as we say here.

Solider

### RE: Rotation Inertia

Solider,

I was being slighly tongue in cheek.  :)

If you do a pile of algebra working out an equation for acceleration, your unit balance should produce units for acceleration.  If you get something like kg.m/s, you have made a mistake somewhere.

If you do not understand the difference between forces and weights, your unit balance tends to be a mess.

JHG

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