# Find CM of a Rod w/ Length & Mass Attached | 3L/4

• I
• bluejay27
In summary, the conversation discusses finding the center of mass (CM) of a rod with mass m and length L, where another mass m is attached at the end. It is mentioned that the CM of the combined system is at 3L/4 and that the original question specified both masses to be of size m. The questioner also asks for clarification on the scenario and if there is a mathematical formula for finding the CM.
bluejay27
How do you find the CM of a rod of length L and mass m that has been attached by another mass m?

It is supposed to be 3L/4

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..

bluejay27
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..
Could you be more explicit? I was imagining a mass of negligible size being attached to it. Is there a mathematical formula?

The original question said that the rod and the attached mass were both mass m.

bluejay27
mathman said:
The original question said that the rod and the attached mass were both mass m.
I got it!

## What is the center of mass (CM)?

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.

## How do you find the center of mass of a rod with length and mass attached?

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.

## What is the equation for the center of mass of a uniform rod?

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.

## How does the distribution of mass affect the center of mass?

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.

## Why is finding the center of mass important in physics?

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.

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