# Center of mass triangle problem

• nicholas1
In summary, the center of mass of a pentagon with one missing triangle can be found by locating the y-coordinate of the combined center of mass of the four remaining triangles along the y-axis, which is the line of symmetry. This can be done by taking the moments of mass of each triangle about a perpendicular x-axis and using the total area of the shape in the calculations. For a circle with one quadrant missing, the center of mass is located \frac{2}{3}R up from the sharp point.
nicholas1
After finding the center of mass of a pentagon with five equal sides a but one triangle missing, then iam asked to find the CM of uniform square a with one quadrant missing.

Wellcome to PF nicholas.

First note that the com will lie along the line of symmetry. This means it will be located along the line through the middle of the pentagon and dividing the missing triangle in half, let's call this line the y-axis. This means that you need to locate the y-coordinate of the combined com of the four triangles along the axis.

To locate the y-coordinate of the combined com of the four triangles you need to take the moments of mass of the com of each of the triangles about a line perpendicular to the y-axis. Let's call it the x-axis. Position it at the base of the pentagon.

For the mass of the coms, and total mass, you just need to consider only the total area of the shape in the moment calculations (that is you assume that the mass can be found by multiplying the area by some constant).

Use the fact that the sum of the mass moments of the coms of the four triangles about the x-axis need to be equal to the moment of the combined com (total area of the four triangles times $$\bar{y}$$) about your x-axis- it is in this equation that the above mentioned constant will cancel out.

The circle with one quadrant is actually much easier! Can you proof that the com of one quadrant is located $$\frac{2}{3}R$$ up from the sharp point?

Last edited:

The center of mass (CM) is a point in an object where its mass can be considered to be concentrated. In the context of this problem, the CM of a pentagon with one missing triangle is the point where the mass of the pentagon is evenly distributed. This can be found by taking the average of the coordinates of each vertex of the pentagon.

To find the CM of a uniform square with one quadrant missing, the same approach can be used. The CM will be the point where the mass of the square is evenly distributed. This can be found by taking the average of the coordinates of each vertex of the square.

It is important to note that the CM is not always located within the physical boundaries of the object. In some cases, it may be outside of the object. Additionally, the CM can change depending on the orientation of the object. Therefore, it is important to specify the reference frame in which the CM is being measured.

I hope this helps clarify the concept of center of mass. If you have any further questions, please feel free to ask.

## 1. What is the center of mass triangle problem?

The center of mass triangle problem is a physics problem that involves finding the center of mass of a triangular object. It is commonly used in mechanics and other fields to determine the overall balance and stability of an object.

## 2. How do you calculate the center of mass of a triangle?

To calculate the center of mass of a triangle, you need to find the average of the x-coordinates and the average of the y-coordinates of the three vertices. This point, known as the centroid, is the center of mass of the triangle.

## 3. What is the significance of the center of mass in a triangle?

The center of mass of a triangle is important because it represents the point at which the entire mass of the triangle can be concentrated. It is also a point of equilibrium, meaning that if the object is supported at the center of mass, it will remain balanced.

## 4. How does the shape of the triangle affect the center of mass?

The shape of the triangle does not affect the location of the center of mass, as long as the triangle is a flat, two-dimensional object. However, if the triangle is three-dimensional, the distribution of mass within the object can affect the location of the center of mass.

## 5. What are some real-life applications of the center of mass triangle problem?

The center of mass triangle problem has many practical applications, such as determining the stability of structures, designing balance points for objects, and understanding the movement of objects in space. It is also used in sports, such as balancing a surfboard or skateboard, and in engineering, such as designing the center of gravity for vehicles.

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