Finding the Centroid of Combined Shapes

  • Thread starter haddow64
  • Start date
  • Tags
    Gravity
In summary, The centroid of a combined shape is the point where their respective center of masses are located.
  • #1
haddow64
14
0
Hi guys, would really appreciate some help with this question, so far I've only been doing really simple c.o.g questions and I'm lost with this one.

A triangle has its vertices at the coordinates (0,0),(0,4) and (6,0). A rectangle has its vertices at the coordinates (0,0),(8,0),(8,-4) and (0,-4). Determine the coordinates of the centroid of the combined shape.


Ok I started out by finding the center of gravity of each separate shape

rectangle (4,-2)
triangle (1.3,2)



But I don't know where to go after this. Can anyone give me some pointers on how to solve this?
 
Physics news on Phys.org
  • #2
If you had two point masses at different points, could you find their combined center of mass? (I hope so.) Same thing here: For the purpose of calculating the center of mass, think of each shape as a point mass located at that shape's center of mass.
 
  • #3
So am i right in thinking that I just find the midpoint between the center of gravity of the triangle and rectangle to get the midpoint of the whole shape?

My brain is working slowly today have been doing maths and physics since mid day almost 9 straight hours :(
 
  • #4
haddow64 said:
So am i right in thinking that I just find the midpoint between the center of gravity of the triangle and rectangle to get the midpoint of the whole shape?
It would only be the midpoint if they have the same mass.

My brain is working slowly today have been doing maths and physics since mid day almost 9 straight hours
I know that feeling all too well. Hang in there.
 
  • #5
Ok so I take moments about the vertical and horizontal edges.

How would I do this? Really stuck here and its the last question I have to do so any help would be really appreciated.
 
  • #6
Do you know the mass of each piece? (Or are you to assume they are of uniform density? If so, their areas will be proportional to their masses.)

Given the masses (or at least the relative masses) you treat this using the definition of the center of mass of several particles. Read this for a review: http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html"
 
Last edited by a moderator:

FAQ: Finding the Centroid of Combined Shapes

1. What is the center of gravity problem?

The center of gravity problem is a physics problem that involves determining the point at which an object's weight is evenly distributed in all directions. It is also known as the center of mass problem.

2. How is the center of gravity calculated?

The center of gravity is calculated by finding the weighted average of the coordinates of all the points that make up an object. This is done by multiplying the coordinates of each point by its mass and then dividing the sum of these products by the total mass of the object.

3. What factors affect the center of gravity?

The center of gravity is affected by the mass and distribution of weight in an object. Objects with more mass or weight distributed further from the center will have a lower center of gravity, while objects with less mass or weight closer to the center will have a higher center of gravity.

4. Why is the center of gravity important?

The center of gravity is important because it determines the stability and balance of an object. An object with a lower center of gravity will be more stable and less likely to tip over, while an object with a higher center of gravity will be less stable and more likely to tip over.

5. How does the center of gravity affect motion?

The center of gravity plays a crucial role in an object's motion. In order for an object to remain in equilibrium, its center of gravity must stay within its base of support. If the center of gravity shifts outside of the base of support, the object will tip over or lose its balance. This is why athletes and dancers must be conscious of their center of gravity to maintain balance and perform precise movements.

Similar threads

How to Find the Centroid of a Composite Shape?
Replies
2
Views
21K
Find the position of the centroid of the shaded area
Replies
17
Views
5K
How do you "read" this formula?
Replies
2
Views
1K
To find the center of gravity of a particular quadrilateral
Replies
12
Views
2K
To find the centre of gravity of a lamina
Replies
2
Views
1K
To find the weight of a hemisphere
Replies
13
Views
1K
Time of Fall in triangular and rectangular frame
Replies
10
Views
1K
How to Find the Second Moment of Area for a Rectangle with a Circular Cutout?
Replies
5
Views
2K
What is the process for finding the moment of inertia for a semicircle?
Replies
6
Views
1K
Find Centroid of Shape: X & Y Dimensions from Point O
Replies
4
Views
3K

Hot Threads

Recent Insights

Back
Top