Rotational Inertias of Different Shapes

In summary, the conversation discusses a question about memorizing or deriving an equation for inertia for an upcoming exam. The solution is to refer to the correct integral and solve it. It is mentioned that deriving an equation for inertia is not typically required in physics studies and it is likely that the equation will be provided on the exam.
  • #1
Meta14
8
0
Sorry, this isn't a question from a book or something, but I wasn't sure where else to put this. Is there a convenient way of memorizing or deriving the following?:

Figure_11_03_06.jpg


I have an exam in a week and I thought I might as well try asking before making flashcards.
 
Physics news on Phys.org
  • #2
Well, you can see, how the inertia is defined by an integral here:
http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html

So basically, it's just about putting up the correct integral and solve it. I did not, however, ever need to actually derive one of them through any of my physics studies. If your teacher hasn't done it, I doubt you will be asked to. If you cannot use books or anything for the exam, I would believe, that an equation for the inertia needed for the specific body will surely be given.
 

FAQ: Rotational Inertias of Different Shapes

1. What is a rotational inertia and how is it different from mass?

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 the sense that it describes an object's inertia, but while mass is a measure of an object's resistance to linear motion, rotational inertia describes its resistance to rotational motion.

2. How is the rotational inertia of different shapes calculated?

The formula for calculating rotational inertia depends on the shape of the object. For example, the rotational inertia of a solid cylinder is given by 1/2 * (mass * radius^2), while the rotational inertia of a hollow cylinder is given by (mass * radius^2). There are different formulas for different shapes, and they can be found in physics textbooks or online.

3. How does the distribution of mass affect an object's rotational inertia?

The distribution of mass plays a significant role in determining an object's rotational inertia. Objects with more mass concentrated towards the center have a lower rotational inertia compared to objects with the same mass but with the mass distributed farther from the center. This is because the mass farther from the center contributes more to the object's rotational inertia.

4. How does the shape of an object affect its rotational inertia?

The shape of an object also affects its rotational inertia. Objects with a larger radius have a higher rotational inertia compared to objects with the same mass but with a smaller radius. This is because the larger radius results in a larger distance from the axis of rotation, which increases the object's resistance to rotational motion.

5. Why is understanding rotational inertia important in physics?

Understanding rotational inertia is crucial in physics because it helps explain how objects behave in rotational motion. It is a fundamental concept in rotational dynamics and is used to predict the motion of objects such as wheels, spinning tops, and planets. Additionally, rotational inertia is also important in engineering, as it is taken into consideration when designing objects that need to rotate or maintain stability.

Similar threads

Replies
13
Views
2K
Replies
32
Views
3K
Replies
4
Views
5K
Replies
7
Views
2K
Replies
3
Views
2K
Replies
4
Views
1K
Back
Top