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brandon26
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Where is the centre of mass of a semicircular lamina which is uniform? I know it is somewhere along the line of symestry, but where excactly?
Finding Centre of Mass for a Uniform Semicircular Lamina
- Thread starter brandon26
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In summary, the center of mass of a semicircular lamina with uniform density is located at 4r/3pi, along the line of symmetry. To find the y-coordinate of the centroid, use the formula \frac{\int y dA}{\int dA}, where \int dA represents the area of the region. Additionally, "lamina" is the word "animal" spelled backwards and can lead to confusion in certain situations.
- #2
Fermat
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It only takes a few moments to work it out.
com = 4r/3pi
com = 4r/3pi
- #3
brandon26
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Can you be of more help please?
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Fermat
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Of course. Drag your mouse over the answer in my last post.
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HallsofIvy
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Surely, if you have a question like that, you know the basic formulas.
The y-coordinate of the centroid of a region (center of mass assuming uniform density) is [tex]\frac{\int y dA}{\int dA}[/tex].
[tex]\int dA[/tex] is, of course, the area of the region.
Once, when I was teaching this, a student became fascinated by the word "lamina" (had never seen it before, apparently). As the last question on the final exam, I asked "What is 'lamina' spelled backwards?"
Another student became furious with me because "That question doesn't make any sense!"
The y-coordinate of the centroid of a region (center of mass assuming uniform density) is [tex]\frac{\int y dA}{\int dA}[/tex].
[tex]\int dA[/tex] is, of course, the area of the region.
Once, when I was teaching this, a student became fascinated by the word "lamina" (had never seen it before, apparently). As the last question on the final exam, I asked "What is 'lamina' spelled backwards?"
Another student became furious with me because "That question doesn't make any sense!"
- #6
brandon26
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Oh sorry. Haha. I didnt realize there was invisible ink on the paper.Fermat said:
1. What is the centre of mass for a uniform semicircular lamina?
The centre of mass for a uniform semicircular lamina is the point at which the lamina would balance if suspended at that point. It is also referred to as the centroid or the center of gravity.
2. How is the centre of mass calculated for a uniform semicircular lamina?
The centre of mass for a uniform semicircular lamina can be calculated using the formula:
x = (4R)/(3π) where R is the radius of the semicircle. This formula gives the x-coordinate of the centre of mass. The y-coordinate will always be at the midpoint of the semicircle.
3. What are the factors that affect the centre of mass for a uniform semicircular lamina?
The centre of mass for a uniform semicircular lamina is affected by the radius of the semicircle, the density of the material, and the shape of the lamina. A larger radius or a higher density will result in a higher centre of mass.
4. Can the centre of mass be outside of the lamina for a uniform semicircular lamina?
No, the centre of mass will always be located within the boundaries of the lamina. This is because the lamina is a closed shape and every point on the lamina has an equal contribution to the centre of mass.
5. How is the centre of mass important in physics?
The centre of mass is an important concept in physics as it helps in understanding the stability and equilibrium of objects. It is also used in various calculations related to motion, such as calculating the torque and momentum of a system.
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