Moment of inertia of a regular triangle

AI Thread Summary
The discussion centers on calculating the moment of inertia of a triangle about the OY axis. The original poster considered splitting the triangle into rods and using the Huygens-Steiner theorem but encountered confusion regarding the correct method of splitting. After some back and forth, it was clarified that using strips parallel to the y-axis was the correct approach, while the alternative method led to errors. The poster acknowledged their mistake and expressed gratitude for the guidance received. The conversation highlights the importance of method selection in physics calculations.
Who_w
Messages
3
Reaction score
2
Homework Statement
Calculate the moment of inertia of a triangle relatively OY
Relevant Equations
Given the height of the triangle
Please, I need help! I need to calculate the moment of inertia of a triangle relatively OY. I have an idea to split my triangle into rods and use Huygens-Steiner theorem, but after discussed this exercise with my friend, I have a question: which of these splits are right (picture 1 and 2)? Or maybe my idea is wrong?
 

Attachments

  • q1.PNG
    q1.PNG
    2.7 KB · Views: 175
  • q2.PNG
    q2.PNG
    2.7 KB · Views: 170
Physics news on Phys.org
Each can work, but it would be more natural to use the one where the strip is parallel to the axis.
 
I found a mistake in the first split, thanks a lot! I would be very grateful if you tell me where the error is (attached the file). With another split, I got a different answer. I solved it 3 times in this way, but did not find an error.
 

Attachments

  • question.jpg
    question.jpg
    57.4 KB · Views: 160
Last edited:
Who_w said:
I found a mistake in the first split, thanks a lot! I would be very grateful if you tell me where the error is (attached the file). With another split, I got a different answer. I solved it 3 times in this way, but did not find an error.
(l-x)dx? Both of those distances are parallel to the x axis. It is not the area of a rectangle in the figure.
Also, you seem to be taking a strip parallel to the x axis, which is not what I recommended. Are you just checking it can be done both ways?
 
haruspex said:
(l-x)dx? Both of those distances are parallel to the x axis. It is not the area of a rectangle in the figure.
Also, you seem to be taking a strip parallel to the x axis, which is not what I recommended. Are you just checking it can be done both ways?
Oh! I understood my mistake! Thank you a lot :)
Yes, I'm tried to check both ways. The first way worked (strip parallel to the y axis), but it was really interesting for me why I couldn't to solve it the second way.
Thanks again!
 
Who_w said:
Oh! I understood my mistake! Thank you a lot :)
Yes, I'm tried to check both ways. The first way worked (strip parallel to the y axis), but it was really interesting for me why I couldn't to solve it the second way.
Thanks again!
I commend your inquisitiveness.
 
Thread 'Voltmeter readings for this circuit with switches'

Thread 'Voltmeter readings for this circuit with switches'

TL;DR Summary: I would like to know the voltmeter readings on the two resistors separately in the picture in the following cases , When one of the keys is closed When both of them are opened (Knowing that the battery has negligible internal resistance) My thoughts for the first case , one of them must be 12 volt while the other is 0 The second case we'll I think both voltmeter readings should be 12 volt since they are both parallel to the battery and they involve the key within what the...
View full post »
Thread 'Correct statement about a reservoir with an outlet pipe'

Thread 'Correct statement about a reservoir with an outlet pipe'

The answer to this question is statements (ii) and (iv) are correct. (i) This is FALSE because the speed of water in the tap is greater than speed at the water surface (ii) I don't even understand this statement. What does the "seal" part have to do with water flowing out? Won't the water still flow out through the tap until the tank is empty whether the reservoir is sealed or not? (iii) In my opinion, this statement would be correct. Increasing the gravitational potential energy of the...
View full post »

Similar threads

Correct Use of the Parallel Axis Theorem for Moment of Inertia
Replies
2
Views
2K
Two objects joined by a rectilinear cable rotating
Replies
8
Views
927
How to calculate the moment of inertia of a bar with two masses on it?
Replies
24
Views
4K
Calculating Moment of Inertia for Hollow Cylinder w/ Water
Replies
40
Views
5K
Moment of inertia, center of mass and vincular reaction of a rod
Replies
16
Views
2K
Parallel Axis Theorem Not Working
Replies
28
Views
1K
What is the "r" in the moment of inertia?
Replies
13
Views
3K
Finding the angular velocity of a pendulum
Replies
3
Views
966
Moment of inertia of a rod bent into a square
Replies
12
Views
2K
Moment of inertia of a cuboid parallel to one of its faces (repost with diagram)
Replies
25
Views
2K

Hot Threads

Recent Insights

Back
Top