Trying to understand moment of inertia; example of a rod

In summary, the moment of inertia of a thin rod of length L about one end is equal to 1/3 times the mass of the rod multiplied by the square of its length. The moment of inertia about the middle of the rod would be 1/12 times the mass of the rod multiplied by the square of its length. This can be derived by setting up the integral for r^2 dm and relating dm with dr. This formula is used to calculate the moment of inertia of a uniform rod with respect to its ends.
  • #1
teng125
416
0
i found smtg that i don't understand.moment of inertia = 1/3 m(r^2) stands for which type pf rod??or reference point??
 
Physics news on Phys.org
  • #2
The moment of inertia of a thin rod of length L about one end is:
[tex]I_{end} = \frac{1}{3} M L^2[/tex]

About the middle, it would be:
[tex]I_{cm} = \frac{1}{12} M L^2[/tex]

(Set up the integral [itex]\int r^2 dm[/itex] and see for yourself!)
 
  • #3
Don't understand something like that. Do the integration by yourself and derive the result. Anyway it is for the moment of inertia of a uniform rod, suppose AB, with respect to its ends A or B.
There is no complication in the integral. Just think about relating dm with dr.
 

Related to Trying to understand moment of inertia; example of a rod

1. What is moment of inertia?

Moment of inertia is a physical property of an object that describes its resistance to rotational motion. It is the measure of an object's tendency to resist changes in its rotational velocity.

2. How is moment of inertia calculated?

The moment of inertia of an object can be calculated by multiplying the object's mass by the square of its distance from the axis of rotation. For example, for a uniform rod rotating about one end, the moment of inertia is equal to 1/3 * mass * length^2.

3. What is an example of moment of inertia for a rod?

An example of moment of inertia for a rod would be a pole vaulter's pole. The pole vaulter's pole is a long, thin rod that is rotated around one end during the pole vault. The moment of inertia for the pole would be calculated using the formula mentioned in the previous answer.

4. Why is moment of inertia important?

Moment of inertia is important because it helps us understand how objects rotate and how much force is needed to change their rotational motion. It is also used in many engineering and physics applications, such as designing machines and predicting the behavior of spinning objects.

5. How does the distribution of mass affect moment of inertia?

The distribution of mass greatly affects the moment of inertia. Objects with more mass located farther from the axis of rotation have a larger moment of inertia, while objects with less mass located closer to the axis have a smaller moment of inertia. This is because the farther the mass is from the axis, the more force is required to change its rotational motion.

Similar threads

  • Advanced Physics Homework Help
Replies
15
Views
1K
  • Advanced Physics Homework Help
Replies
4
Views
1K
  • Advanced Physics Homework Help
Replies
5
Views
973
  • Introductory Physics Homework Help
Replies
2
Views
701
  • Advanced Physics Homework Help
Replies
2
Views
2K
  • Advanced Physics Homework Help
Replies
3
Views
3K
  • Introductory Physics Homework Help
Replies
11
Views
338
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
21
Views
1K
  • Introductory Physics Homework Help
Replies
16
Views
1K
Back
Top