Centre of mass of a solid hemisphere (Feynman way)

  • #1

saturn_1995

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reference to Feyman lectures vol.1 topic 19.2 locating centre of mass

Feyman gives us the law of pappus to find the centre of mass ,which he proves for semicircular disc and ring.

But when i am trying to extend it to finding the centre of mass of a solid semi-circular solid hemisphere ,i seem to get a different answer from what i get from calculus which is 3R/8.

My approach to problem is using law of pappus extensively:-

1. I assume a solid semi-circular hemisphere into infinite number of semi-circular disc, find each disc's centre of mass using law of pappus.
2. I get a ring with all centre of mass of respective discs.
3. using that ring and law of pappus again i find the centre of mass of that ring.

this value which i find doesn't correspond to 3R/8. is there something wrong in my approach
 
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  • #2
It would help if you showed the numerical details of your calculation.
 

1. What is the centre of mass of a solid hemisphere?

The centre of mass of a solid hemisphere is the point at which the entire mass of the hemisphere can be considered to be concentrated. It is the average location of the mass of the hemisphere.

2. How is the centre of mass of a solid hemisphere calculated?

The centre of mass of a solid hemisphere can be calculated using the formula x̄ = 3R/8, ȳ = 3R/8, z̄ = 3R/16, where R is the radius of the hemisphere. This formula is derived using integration and the principles of symmetry.

3. What is the significance of the centre of mass of a solid hemisphere?

The centre of mass of a solid hemisphere is important because it can help determine the overall stability and balance of the hemisphere. It is also useful in solving problems involving rotational motion.

4. How does the centre of mass of a solid hemisphere differ from that of a hollow hemisphere?

The centre of mass of a solid hemisphere and a hollow hemisphere will be in the same location, as long as they have the same radius. However, the mass distribution around the centre of mass will be different for the two shapes.

5. Can the centre of mass of a solid hemisphere be outside of the object?

No, the centre of mass of a solid hemisphere will always be located within the object. This is because the centre of mass is the point at which the mass of the object is evenly distributed, and for a solid hemisphere, all of its mass is contained within its boundaries.

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