The center of mass of a system of particles is the point at which the total mass of the system is concentrated. This point is also known as the center of gravity.

The center of mass and the center of gravity are the same point. This is because the center of gravity is defined as the point at which the total force of gravity acting on a body is zero. Since the total mass of a body is concentrated at its center of mass, the center of gravity must also be at the center of mass.

To find the center of mass of a system of particles, you add up the masses of all the particles and divide by the number of particles. This gives you the average position of the particles in the system.

The center of mass of a uniform rod is the midpoint of the rod. This is because the mass of the rod is evenly distributed along its length.

The center of mass of a sphere is the center of the sphere. This is because the mass of the sphere is evenly distributed throughout its volume.

The center of mass of a hollow sphere is the center of the sphere. This is because the mass of the sphere is evenly distributed throughout its volume, even though there is no mass at the center of the sphere.

The center of mass of a rectangular prism is the center of the prism. This is because the mass of the prism is evenly distributed throughout its volume.

The center of mass of a triangular prism is the midpoint of a diagonal of the prism. This is because the mass of the prism is not evenly distributed throughout its volume.

The center of mass of a cylinder is the center of the cylinder. This is because the mass of the cylinder is evenly distributed throughout its volume.

The center of mass of a cone is one-third of the way from the base to the vertex of the cone. This is because the mass of the cone is not evenly distributed throughout its volume.

The center of mass of a hemisphere is three-eighths of the way from the base to the vertex of the hemisphere. This is because the mass of the hemisphere is not evenly distributed throughout its volume.

The center of mass of a quarter-circle is two-thirds of the way from the center to the edge of the quarter-circle. This is because the mass of the quarter-circle is not evenly distributed throughout its area.

The center of mass of a semi-circle is three-eighths of the way from the center to the edge of the semi-circle. This is because the mass of the semi-circle is not evenly distributed throughout its area.

The center of mass of a triangle is the intersection of the medians of the triangle. This is because the mass of the triangle is evenly distributed throughout its area.

The center of mass of a trapezoid is the intersection of the diagonals of the trapezoid. This is because the mass of the trapezoid is evenly distributed throughout its area.