Moment of Inertia and units

RundleSeb

Summary
Calculating moment of inertia and translating it between units
Calculating moment of inertia and translating it between units, I've become confused.

The example is a mass of 1kg at 2000mm from the pivot. The force is applied at 1000mm from the pivot.

Basics as far as i'm aware:
Moment of inertia = mass * Distance to center of rotation^2
Torque = Moment of inertia * angular acceleration.
Torque = Force* The distance of the force to the center of rotation

so to achieve acceleration of 1 rad/sec^2

In meters
Moment of inertia = 1*(2^2) = 4 kg m^2
Torque = Moment of inertia * angular acceleration = 4*1 = 4 Nm
Force = 4 NM / 1m = 4N

In mm

Moment of inertia = 1*(2000^2) = 4000,000 kg mm^2
Torque = Moment of inertia * angular acceleration = 4000,000*1 = 4000,000 Nmm
Force = 4000,000 NM /1000 mm = 4000N

Can the calculation not be done in distance units other than meters? am I missing something?

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mjc123

Torque units are wrong. 1 kg mm2/s2 ≠ 1 N mm.

RundleSeb

I assume as such, but I can't find equations other than those.

mjc123

But you can do the units conversion, can't you? That's all that's wrong.

RundleSeb

Hmm

Force = mass*acceleration = mass*(distance/time^2)
Force * distance = mass*distance^2 * 1/time^2

It seems the units do kinda add up? I think?

RundleSeb

After a bit of thought over the units , I currently believe this discrepancy is because

1 N = 1 (kg*m)/s^2
thus 1 N = 1000 (kg*mm)/s^2 (or, 1 (kg*mm)/s^2 = 1μN)

Thus considering the earlier question,
Torque (Nmm) = Moment of inertia (kg*mm^2) * angular acceleration(1/s^2) = 4000,000*1 = 4000,000 (μN mm) or 4000 (N mm)

mjc123

Force = mass*acceleration = mass*(distance/time^2)
Force * distance = mass*distance^2 * 1/time^2

It seems the units do kinda add up? I think?
That's dimensions, not units. A picometre and a light year both have dimensions of length, but have very different magnitudes.
Your last post is not quite right. (It might just be a typo)
4,000,000 kg mm2 * 1 s-2 = 4,000,000 kg mm s-2*mm = 4,000,000 mN mm = 4000 N mm = 4 N m.

RundleSeb

Ah i get what you were going at now.

Also well spotted (it is a typo , should be mN not μN)

"Moment of Inertia and units"

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