Understand Rotational Inertia for AP Physics C

In summary: In fact, the definition of inertia in physics texts often goes further and defines inertia as the mass*length*time derivative of the angular velocity (in radians/s), but that's a bit of a rabbit hole for another discussion.In summary, the book from when I studied for the AP physics B test has all the Physics C stuff in it, but it does not make sense conceptually how inertia works at an area.
  • #1
GoldPheonix
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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?
 
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  • #2
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"
 
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  • #3
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 resistence to movement at a point, no?
 
  • #4
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.
 
  • #5
GoldPheonix said:
My only thing is the actualy units of the description: kg*m^2

It is just an odd unit for describing an objects resistence 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.
 

Related to Understand Rotational Inertia for AP Physics C

1. What is rotational inertia?

Rotational inertia, also known as moment of inertia, is a measure of an object's resistance to rotational motion. It is similar to mass in linear motion, but instead applies to rotational motion.

2. How is rotational inertia calculated?

The formula for rotational inertia is I = mr², where I is the rotational inertia, m is the mass of the object, and r is the distance from the axis of rotation to the object.

3. What is the difference between rotational inertia and moment of inertia?

Rotational inertia and moment of inertia are two terms used interchangeably to describe the same concept. They both refer to an object's resistance to rotational motion.

4. How does rotational inertia affect an object's motion?

The greater the rotational inertia of an object, the more difficult it is to change its rotational motion. This means that an object with a higher rotational inertia will require more torque to accelerate or decelerate.

5. What is the importance of understanding rotational inertia in AP Physics C?

Understanding rotational inertia is crucial in AP Physics C as it is a fundamental concept that is used to analyze rotational motion and solve problems related to rotational dynamics. It is also important in understanding concepts such as angular momentum and torque.

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