Question Video: Determining SI Unit for the Moment of Inertia Physics

Which of the following correctly shows the SI unit for the moment of inertia? [A] kg/m² [B] kg².m [C] kg².m² [D] kg.m² [E] (kg.m²)


Video Transcript

Which of the following correctly shows the SI unit for the moment of inertia? (A) Kilograms per meter squared, (B) kilograms squared times meters, (C) kilograms squared times meter squared, (D) kilograms times meter squared, (E) the quantity kilograms times meters squared.

Considering this question, we can see that we’re not talking about moment of inertia for a particular shape, rotating about a particular axis. But instead we’re speaking of this term in general; we want our answer to give the units that apply to all moments of inertia. Along these lines, we can recall that this term, moment of inertia, applies to a mass that’s rotating. In general, the equation for the moment of inertia of a particular mass rotating about a particular axis depends on those two values. But nonetheless, it is true that all moments of inertia share the same SI base units. One way then to identify which of our five options is correct is to recall the equation for the moment of inertia of any shape rotating about any axis.

Perhaps the simplest moment of inertia we can recall is that of a point mass, where that mass is in rotation about an axis a distance 𝑟 away. The moment of inertia of this point mass is its mass 𝑚 times that distance 𝑟 squared. Now, like we said, not all moments of inertia have the same form. In fact, most are different. But they do all have the same units that this one has. And considering the units of this expression, we know that the SI base units of mass are kilograms and that the SI base unit of distance is the meter. So we have some mass in kilograms multiplied by some distance in meters squared, which means that our units for this expression will be kilograms times meter squared.

And like we said, these units apply not just to the moment of inertia of a point mass, but to all moments of inertia. Looking over our answers, we see that option (D) matches up with what we found. And so we choose this as our answer. Kilograms times meter squared are the correct SI units for moment of inertia.

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