How to find moments and center of mass for a given shape using integration?

Click For Summary
To find the moments Mx and My and the center of mass for a lamina with density ρ = 4, the values calculated are Mx = 2, My = 12, and the center of mass at (x, y) = (2, 1/3). The formulas for these calculations can be found on a referenced educational site. The shape in question is defined by the function f(x) = 1/3x. The original poster successfully derived the answers but seeks a proof for the calculations as their textbook does not provide one. This discussion emphasizes the importance of understanding the integration process behind these calculations.
tnutty
Messages
324
Reaction score
1
Not really a homework problem but related. In one of my homework problem, it says ,
Calculate the moments Mx and My and the center of mass of a lamina with density ρ = 4 and the given shape.
Mx = 2
My = 12
(x, y) = (2,1/3 )

I got the answer. YOUR WELCOME.


But, I only got it because I looked up the formula to find Mx,My and (x,y).
the formula is given in this site near the intro http://www.math.utep.edu/Faculty/javila/Calculus%20II/Math%201312%20problems%20for%20section%207.6.pdf

But I was hoping one of you could prove this, since my book didn't.
 
Last edited by a moderator:
Physics news on Phys.org
What is the given shape?
 
it is a function of f(x) = 1/3x.
 

Thread 'Distance between a Clock's hands when the distance is increasing most rapidly'

Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?
View full post »

Similar threads

Calc 3 Moments and centers of mass
  • · Replies 2 ·
Replies
2
Views
6K
Integrals to Solve Area and Center of Mass of a Cut Circle
  • · Replies 10 ·
Replies
10
Views
5K
Finding center of mass of solid
  • · Replies 1 ·
Replies
1
Views
2K
Find center of mass and coordinates using double integrals?
  • · Replies 5 ·
Replies
5
Views
7K
How do you find the centroid of this?
  • · Replies 4 ·
Replies
4
Views
2K
Finding the Centre of Mass of a Hemisphere
  • · Replies 13 ·
Replies
13
Views
3K
Center of Mass of a Sphere with uniform density
  • · Replies 19 ·
Replies
19
Views
6K
Moments,Center of Mass, & Centroid
  • · Replies 1 ·
Replies
1
Views
5K
Use triple integral to find center of mass
  • · Replies 7 ·
Replies
7
Views
3K
Calculus: Moments-Are these correct ?
  • · Replies 1 ·
Replies
1
Views
2K