Moment of Inertia: Proving Mass, Side & Axis | 1/12 md²

AI Thread Summary
To prove that the moment of inertia of a uniform square of mass m and side d about an axis through its center, parallel to a side, is 1/12 md², one must use the definition of moment of inertia, which involves integration. The discussion emphasizes the importance of setting up the correct integral for the calculation. Participants encourage the user to write out the integral and attempt the integration process to derive the proof. Clarification on the procedure is provided, indicating that the outcome of the integration will serve as the proof needed. Engaging in this methodical approach will help solidify understanding of the concept.
Chadi B Ghaith
Messages
35
Reaction score
4
I need help to prove that the moment of inertia of a uniform square of mass m and side d about an axis through its centre, parallel to a side is 1/12 md²
 
Physics news on Phys.org
Chadi B Ghaith said:
I need help to prove that the moment of inertia of a uniform square of mass m and side d about an axis through its centre, parallel to a side is 1/12 md²
OK, what kind of help ? You know the definition of moment of inertia ? It amounts to an integration; does that pose a problem ? Write it out and we'll help you further.
 
BvU said:
OK, what kind of help ? You know the definition of moment of inertia ? It amounts to an integration; does that pose a problem ? Write it out and we'll help you further.
Hi,
Yes I know the definition of inertia. What I am asking is how to prove the above statement. I am bit confuse in procedure.
 
Good you know it. Write down the integral and attempt to do the integration in your next post. The outcome of your calculation is your 'proof'.
 

Thread 'Is calling fictitious forces "not real" just about terminology?'

Hi there, im studying nanoscience at the university in Basel. Today I looked at the topic of intertial and non-inertial reference frames and the existence of fictitious forces. I understand that you call forces real in physics if they appear in interplay. Meaning that a force is real when there is the "actio" partner to the "reactio" partner. If this condition is not satisfied the force is not real. I also understand that if you specifically look at non-inertial reference frames you can...
View full post »

Thread 'Derivation of Hamilton's Principle: Questions'

I have recently been really interested in the derivation of Hamiltons Principle. On my research I found that with the term ##m \cdot \frac{d}{dt} (\frac{dr}{dt} \cdot \delta r) = 0## (1) one may derivate ##\delta \int (T - V) dt = 0## (2). The derivation itself I understood quiet good, but what I don't understand is where the equation (1) came from, because in my research it was just given and not derived from anywhere. Does anybody know where (1) comes from or why from it the...
View full post »

Similar threads

I Resolve moment of inertia at an angle
Replies
2
Views
2K
I Explanation of parallel axis theorem
Replies
2
Views
1K
I Moment of inertia of human body with limbs at an angle
Replies
12
Views
2K
I Moment of Inertia about an axis and Torque about a point
Replies
5
Views
3K
B Moment of Inertia of Rectangles
Replies
3
Views
3K
I Inertia of body moving about two distinct parallel axes
Replies
10
Views
2K
I Calculating Mass Inertia Product - Examples 1 & 2
Replies
2
Views
2K
How can I calculate the moment of inertia of any object?
Replies
10
Views
2K
Why Do Different Objects Share Similar Moments of Inertia?
Replies
1
Views
2K
Does mass distribution affect an object's ease of rotation?
Replies
13
Views
2K

Hot Threads

Recent Insights

Back
Top