# Find CM of Round Bottom Cone | Centre of Mass Problem

• Gogsey
In summary, the conversation discusses how to find the center of mass (CM) for a round spherical bottomed cone by breaking it up into a regular cone and a hemisphere. Superposition can be used to find the individual CMs for each part, and then they can be combined to find the overall CM for the object. The location of the origin does not matter, but a convenient location would be where the two parts meet and intersect with the line of symmetry. The CMs of the individual parts can be treated as point masses to find the CM of the entire object.
Gogsey
Is there anyway of breaking up the parts of an a round spherical bottomed cone into a regular cone and a hemisphere?

I can find the CM of a cone with its tip on the origin, and a hemisphere with its flat bottom in the x-y plane. Can I break the round bottomed cone up into these 2 parts? How would I go about combining them to find the CM of the round bottomed cone?

The z-axis goes though the centre of the round bottomed cone lengthways.

Yes, superposition can be used to find the CM of the object. Find the CM of the hemisphere then find the CM of the cone using a common coordinate system. These two locations can treated as point masses then be used to find the CM of the object.

Does that mean I can but the flat bottom of the hemisphere at the origin, and the tip of the cone at the origin? Or do I have to put say the cone tip at the origin, and the flat bottom of the hemisphere at the top of the cone?

So then how do I find the combined CM for the object?

It does not matter where you place the origin but a convenient location would be where the cone and hemisphere meet and intersect with the line of symmetry. To answer your second question, how would you find the CM of two point objects?

## 1. What is the formula for finding the center of mass (CM) of a round bottom cone?

The formula for finding the CM of a round bottom cone is (3r/4h, 3r/4h, 3r/8), where r is the radius of the base and h is the height of the cone.

## 2. How do you determine the mass of a round bottom cone?

To determine the mass of a round bottom cone, you need to know the density of the material it is made of and its volume. The mass can then be calculated using the formula mass = density * volume.

## 3. Can the CM of a round bottom cone be outside the cone?

Yes, the CM of a round bottom cone can be outside the cone. This can happen if the density is not evenly distributed throughout the cone or if the cone is not symmetric.

## 4. What is the significance of finding the CM of a round bottom cone?

Finding the CM of a round bottom cone is important in understanding the stability and balance of the cone. It can also be useful in engineering and design, as well as in physics and other related fields.

## 5. How is the CM of a round bottom cone related to its center of gravity?

The CM and center of gravity (CG) of a round bottom cone are the same point. This is because the CM is the point where the mass of the cone is evenly distributed, and the CG is the point where the weight of the cone is evenly distributed. In a symmetric cone with uniform density, the CM and CG will be at the same point.

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