Understand Rotational Inertia for AP Physics C

[GoldPheonix]

I am probably not taking the AP physics C tests, but I have the book from when I studied by myself for the AP physics B test, and it has all the Physics C stuff in there as well.

Now, with that said, there is a section in rotational motion. Most of it makes perfect sense mathematically, but I just do not get conceptually how:

I = rotational intertia
M = mass
r = radius

I = M*r^2


That's like what, inertia at an area? It just seems to make such little conceptual sense. Does anyone have a better way of thinking about rotational inertia?

 

[Doc Al]

Think of rotational inertia as the rotational analog to mass. Just as mass measures an object's resistance to changes in linear acceleration, rotational inertia measures an object's resistance to changes in angular (rotational) acceleration. For a discussion of how to make sense of that formula (I = mr^2, the rotational inertia of a point mass) read this: http://hyperphysics.phy-astr.gsu.edu/hbase/mi2.html#rlin"

 

[GoldPheonix]

Yeah, I've seen how it works in math (I'm so much better at math than at concepts), but the analog escription seems to make a little bit more sense.

My only thing is the actualy units of the description: kg*m^2

It is just an odd unit for describing an objects resistance to movement at a point, no?

 

[Cyrus]

Inertia is a mathematical definition used as a simplification because it comes up in many other areas of physics. Don't try to put a physical interpretation into it. It is just defined that way because it is a useful definition so you can have I's in your equations and not MR^2. There is even a moment of area which had the units of length^4. Like I said, it has no physical meaning.

 

[Doc Al]

My only thing is the actualy units of the description: kg*m^2

It is just an odd unit for describing an objects resistance to movement at a point, no?

Well, no. If you read the link, and see rotational inertia as the rotational analog to mass, where in Newton's 2nd law torque (units: N-m) replaces force (units: N) and angular acceleration (units: 1/s^2) replaces linear acceleration (units: m/s^2), then rotational inertia must have those units for the equation to make sense.