What is moment of inertia?

Analog
2023-09-23 21:19:07

In a state of bewilderment one fine day, I asked a group of three mechanical engineers at this company where I was then employed if they could please explain to me the concept of “moment of inertia”. To my utter astonishment, none of them could offer an explanation. None of them knew!

Since then, though, I think I’ve found out.

Sir Isaac Newton taught us (please forgive my paraphrasing) that for linear motion of some object, we have F = m*A which means that a mass “m” will undergo a changing linear velocity at some value of acceleration “A” under the influence of an applied force “F”.

Figure 1 Linear motion on a frictionless surface where force is equal to mass multiplied by acceleration. Source: John Dunn

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There is an analogous equation for rotary motion. We have T = J*Θ where “T” is the torque applied to some object having a moment of inertia “J” which experiences a rotary acceleration called “Θ” which can be measured in units of radians per second squared.

Figure 2 Rotary Motion where the torque applied to an object is equal to its moment of inertia about the rotation axis multiplied by its rotary acceleration. Source: John Dunn

In a rotary motor, the armature will have some particular moment of inertia. There will also be a motor coefficient of torque designated kt. The torque that gets created within that motor will be kt multiplied by the armature current. In short, we will have T = kt*I where I is the armature current.

Writing further, we have kt*I = J* Θ which rearranges to Θ = kt I / J = Angular acceleration.

Angular acceleration is directly proportional to the applied armature current times the coefficient of torque and inversely proportional to the moment of inertia.

John Dunn is an electronics consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York University (MSEE).