Finding center of mass of a right triangle

Click For Summary
SUMMARY

The center of mass for a right triangle with base length 1 and height length 2, weighing 5 kg, can be determined using the centroid formula. The area of the triangle is calculated using the formula A = (1/2) * base * height, which results in an area of 1 square unit. For a uniform density, the center of mass coincides with the centroid, located at coordinates (1/3, 1/6) from the right angle vertex. This approach utilizes integral calculus to confirm the centroid's position in a uniform gravitational field.

PREREQUISITES
  • Understanding of integral calculus
  • Familiarity with the centroid formula for geometric shapes
  • Knowledge of the area calculation for triangles
  • Basic principles of physics regarding mass and density
NEXT STEPS
  • Study the centroid formulas for various geometric shapes
  • Learn how to apply integral calculus to find centers of mass
  • Explore the concept of uniform density in physical systems
  • Review statics textbooks for additional examples of center of mass calculations
USEFUL FOR

Students in physics or engineering courses, educators teaching statics, and anyone interested in understanding the principles of center of mass in geometric shapes.

vande060
Messages
180
Reaction score
0

Homework Statement



Find the center of mass for the following triange:

http://www.ehow.com/how_5132033_calculate-hypotenuse.html

above is a picture of a triangle, it is a right triangle

the side labeled a in the picture is a length of 1 and side b is length of 2, the total weight of the triangle is 5kg.



Homework Equations



a = bh*1/2



The Attempt at a Solution



I don't know much about where to begin, except for that this problem is an integral problem, somehow involving the area of a triangle formula, and the formula for density.
 
Physics news on Phys.org
Yes, its technically an integral. Actually one integral for each dimension x & y,
but for a uniform density and gravitational field, the center of mass will be equal to the centroid of area. These formulas for a triangle are quite common and should be able to be found in any statics book or online easily.
 

Similar threads

Finding the center of mass of a simple 2D shape
  • · Replies 9 ·
Replies
9
Views
3K
Help Me Solve My Diagram Problem: Calculating Center of Mass
  • · Replies 8 ·
Replies
8
Views
3K
Centroid of an isoceles triangle
  • · Replies 1 ·
Replies
1
Views
2K
Problem when calculating the center of mass of a triangle
  • · Replies 5 ·
Replies
5
Views
2K
Finding the center of mass of an arbitrary uniform triangle
  • · Replies 20 ·
Replies
20
Views
8K
Calculating Center of Mass in NH3 Molecule
  • · Replies 4 ·
Replies
4
Views
8K
Understanding a Velocity-Time Graph
  • · Replies 14 ·
Replies
14
Views
6K
Calculus 2 - Center of Mass and Pappus Centroid Theorem
  • · Replies 1 ·
Replies
1
Views
2K
Finding the Center of Mass of a Triangle
  • · Replies 2 ·
Replies
2
Views
4K
Magnetic field of off center triangle - Biot Savart Law
  • · Replies 1 ·
Replies
1
Views
4K