Determine the position of centre of mass of semicircular ring
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Total mass of that semicircular disc is given to be "m" and radius "r" so To detect position of centre of mass of semicircular disc we will use following formula y coordinate of centre of mass=∫mass of that small semicircular ring multiplied by Y coordinate of it's centre of mass/∫dm(mass of that small semicircular ring ) Now mass of the small ring would be equal mass per unit area multiplied by area of ring i.e 2m/π r^2 multiplied by circumference by thickness i.e πp dp.Y coordinate of the ring can be treated as Y coordinate of it's centre of mass .In one of our derivations Y coordinate of semicircular ring came out to be 2 multiplied by it's radius/π So y coordinate of centre of mass=∫2m/π r^2 multiplied by πp dp ×2pπ/ ∫dm an integration has upper and lower limit of r and zero respectively because we want to take all possible small rings of "0" to "r" radius. = So centre of mass of semicircular disc will be 4r/3 pi vertical distance from origin.I understood all these except how thickness comes out to be dp?How thickness can be derivative of radius(dR)?
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