Could you be more explicit? I was imagining a mass of negligible size being attached to it. Is there a mathematical formula?mathman said:Cm of rod is at L/2. Attach (assume at the end) another mass of the same size. Cm of rod plus mass is at average position = 3L/4..
I got it!mathman said:The original question said that the rod and the attached mass were both mass m.
The center of mass (CM) is a point in an object or system where the mass is evenly distributed in all directions. It is the average position of all the mass in the object.
To find the center of mass of a rod with length and mass attached, you can use the formula: CM = (m1*x1 + m2*x2 + m3*x3 +...)/(m1 + m2 + m3 +...), where m is the mass and x is the position of each individual mass. In this case, the rod can be divided into smaller segments with a known mass and position, making it easier to calculate the CM.
The equation for the center of mass of a uniform rod is CM = L/2, where L is the length of the rod. This means that the center of mass of a uniform rod is located at the halfway point.
The distribution of mass affects the center of mass because the CM is calculated based on the position and mass of each individual part of the object. If the mass is evenly distributed, the CM will be in the center of the object. However, if the mass is concentrated in one area, the CM will be closer to that area.
Finding the center of mass is important in physics because it helps determine the overall motion of an object or system. The CM is the point where all external forces can be considered to act on the object, making it useful in calculating the object's motion and stability.