Scribd
Upload
51 views1 page

Definitions

A body has a center of gravity G, which is the single point where the total weight of all particles in the body is concentrated. The location of the center of gravity G can be calculated using integrals of the particle coordinates and weights over the body. Similarly, the centroid or geometric center of a body, area, or line can be calculated using integrals of the coordinates over volume, area, or length, respectively.

Uploaded by

Mohammad Umair
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
51 views1 page

Definitions

A body has a center of gravity G, which is the single point where the total weight of all particles in the body is concentrated. The location of the center of gravity G can be calculated using integrals of the particle coordinates and weights over the body. Similarly, the centroid or geometric center of a body, area, or line can be calculated using integrals of the coordinates over volume, area, or length, respectively.

Uploaded by

Mohammad Umair
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as DOCX, PDF, TXT or read online on Scribd
You are on page 1/ 1

Center of Gravity

A body is composed of an infinite number of particles of differential size, and so if the body is located within a
gravitational field, then each of these particles will have a weight 𝑑𝑊. These weights will form an approximately
parallel force system, and the resultant of this system is the total weight of the body, which passes through a single
point called the center of gravity, G.

The location of the center of gravity G with respect to the x , y , z axes becomes
∫ 𝑥̃ 𝑑𝑊 ∫ 𝑦̃ 𝑑𝑊 ∫ 𝑧̃ 𝑑𝑊
𝑥̅ = 𝑦̅ = 𝑧̅ =
∫ 𝑑𝑊 ∫ 𝑑𝑊 ∫ 𝑑𝑊
Here
𝑥̅ , 𝑦̅, 𝑧̅, are the coordinates of the center of gravity G
𝑥̃, 𝑦̃, 𝑧̃ , are the coordinates of each particle in the body

Centroid or Geometric Center of A Body


∫ 𝑥̃ 𝑑𝑉 ∫ 𝑦̃ 𝑑𝑉 ∫ 𝑧̃ 𝑑𝑉
𝑥̅ = 𝑉 𝑦̅ = 𝑉 𝑧̅ = 𝑉
∫𝑉 𝑑𝑉 ∫𝑉 𝑑𝑉 ∫𝑉 𝑑𝑉
If the volume possesses two planes of symmetry, then its centroid must lie along the line of intersection of these two
planes.

Centroid of an Area
∫𝐴 𝑥̃ 𝑑𝐴 ∫𝐴 𝑦̃ 𝑑𝐴
𝑥̅ = 𝑦̅ =
∫𝐴 𝑑𝐴 ∫𝐴 𝑑𝐴

Centroid of a Line
∫𝐿 𝑥̃ 𝑑𝐿 ∫𝐿 𝑦̃ 𝑑𝐿
𝑥̅ = 𝑦̅ =
∫𝐿 𝑑𝐿 ∫𝐿 𝑑𝐿

You might also like