Category: Moment of Inertia and Centroid

Considering a semicircle of radius R as shown in Figure 11.10. Due to symmetry centroid must lie on y-axis. Let its distance from the x-axis be . To find , consider an element at a distance r from the centre O of the semicircle, radial width dr, and bound by radii at θ and θ + dθ. Figure 11.10 Centroid of Circular Section of a Disc Area of the element = rdθ dr. Its…

Centroid of an arc of a circle, as shown in Figure 11.9, has length L = R·2α. Let us consider an element of the arc of length dL = Rdθ. Figure 11.9 Centroid of Circular Arc

The T-section, shown in Figure 11.8, can be divided into two parts: lower and upper parts of area A1 and middle part of area A2. The lengths and widths of all the parts of L-section are shown in Figure 11.8. Let the X and Y coordinates pass through origin O. Figure 11.8 C-section The coordinates…

The T-section, shown in Figure 11.7, can be divided into two parts: lower part of area A1 and upper part of area A2. The lengths and widths of all the parts of L-section are shown in Figure 11.7. Let the X and Y coordinates pass through origin O. Figure 11.7 T-section The coordinates for centroid can be calculated using the following formula:

The L-section, shown in Figure 11.6, can be divided into two parts: lower part of area A1 and upper part of area A2. The lengths and widths of all the parts of L-section are shown in Figure 11.6. Let the X and Y coordinates pass through origin O. Figure 11.6 L-section The coordinates for centroid can be calculated using the following formula:

The L-section, shown in Figure 11.6, can be divided into two parts: lower part of area A1 and upper part of area A2. The lengths and widths of all the parts of L-section are shown in Figure 11.6. Let the X and Y coordinates pass through origin O. Figure 11.6 L-section The coordinates for centroid can be calculated using the following formula:

The U-section shown in Figure 11.4 can be divided into three parts—lower part of area A1 and two upper parts of area A2. The lengths and widths of all the parts of U-section are shown in Figure 11.4. Let the X and Y coordinates pass through origin O. Figure 11.4 U-section The coordinates for centroid can be calculated using the following formula:

The I-section, shown in Figure 11.2, can be divided into three parts—lower part of area A1, middle part of area A2, and upper part of area A3. The lengths and widths of all the parts of I-section are shown in Figure 11.2. Let the X and Y coordinates pass through origin O as shown in Figure 11.3. Figure 11.2 Centroid of I-section Figure 11.3 Reference Axes for I-section The coordinates for centroid can be…

In Figure 11.1, an irregular shape is shown for which we want to calculate the centre of gravity, centre of mass, and centroid. Here, our purpose is to differentiate the concepts of these three different terms. It is assumed that the irregular shape, as shown in Figure 11.1, is of uniform thickness, density, and subjected to uniform gravitational field.…

The centroid of an area is the mean position of elements of area. The coordinates of centriod is mean value of coordinates of all the elemental points in the area. The centre of mass is the mean position of elements of mass. In a uniform gravitational field, the gravitational force acts through the centre of…