Various Formulas for Centre of Mass
Some systems occur more frequently in real life than others. While calculating the Centre of mass for such systems, the traditional method takes time. Certain centres of mass formulas should be kept in mind while solving the questions related to the Centre of mass. These formulas help in simplifying the calculations.
Center of Mass of System of Two Point Masses
In such a system, COM lies closer to the heavier mass.
m1r1 = m2r2
Distance of COM from mass m1 = [Tex]\frac{m_2r}{m_1 + m_2} [/Tex]
Distance of COM from mass m2 = [Tex]\frac{m_1r}{m_1 + m_2} [/Tex]
Centre of Mass of Triangle
The centre of mass of any triangle of height h is at a distance h/3 from its base. If we take a uniform triangle of height h then its centre of mass is at, height h/3 from the base. The image added below shows the same,
Centre of mass of the triangle lies at the point, which is at the height of h/3
Centre of Mass of Triangle = h/3
where h is the height of the Triangle.
Centre of Mass of Semicircular Disk
The centre of mass of any semi-circular disc of radius r is at a distance of 4r/3π from its base. If we take a uniform semi-circular disc of radius r then its centre of mass is at, height 4r/3π from the base. The image added below shows the same,
Centre of mass of the semi-circular disc lies at the point, which is at the height of 4r/3π
Centre of Mass of Semi-Circular Disc = 4r/3π
where r is the radius of the semi-circular disc
Center of Mass of Half Ring
The centre of mass of any half ring of radius r is at a distance of 2r/π from its base. If we take a uniform semi-circular disc of radius r then its centre of mass is at, height 2r/π from the base. The image added below shows the same,
Centre of mass of the half-ring lies at the point, which is at the height of 2r/π
Centre of Mass of half-ring = 2r/π
where r is the radius of the half-ring.
Centre of Mass of Solid Hemisphere
The centre of mass of a solid hemisphere is located at the intersection of its axis of symmetry and the plane of its circular base. To find the coordinates of the centre of mass of a solid hemisphere of radius R and uniform density, we can use the following formula:
xcm = (3R)/(8π)
The y-coordinate and z-coordinate of the centre of mass are both zero.
Centre of Mass of Solid Cone
The center of mass of a solid cone is located along its axis of symmetry, at a distance of 3/4 times the height of the cone from its base.
To find the coordinates of the centre of mass of a solid cone of radius R, height H, and uniform density, we can use the following formula:
xcm = (3H)/(4π)
The y-coordinate and z-coordinate of the centre of mass are both zero.
Centre of Mass of Hollow Cone
The center of mass of a hollow cone is located along its axis of symmetry, at a distance of 1/4 times the height of the cone from its base.
To find the coordinates of the centre of mass of a hollow cone of radius R, height H, and uniform density, we can use the following formula
xcm = (H/4)(1 + (R/ro)2)
Centre of Mass
Centre of Mass is the point of anybody where all the mass of the body is concentrated. For the sake of convenience in Newtonian Physics, we take the body as the point object where all its mass is concentrated at the centre of mass of the body. The centre of mass of the body is a point that can be on the body such as in the case of a Circular sheet, rectangle sheet, sphere, etc, and can also be outside the body such as in the case of a ring, hollow sphere, etc.
In this article, we’ll explore the basic fundamentals of the centre of mass, including its definition, methods, and formula to calculate it. We’ll also discuss some real-world examples of the centre of mass to help you see its practical applications. So, let’s start learning about the fascinating world of the centre of mass and its role in the physics of motion.