Find the centre of mass of a uniform plate having semicircular inner and outer boundaries of radii r1 and r2 "sarthak"
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Theory is That first it's a plate
That means it will have area
Let the Bigger radius Disc have Area πr2²/2 (r2 means outer radius and not r* 2) ( why Did I divide by two ? cuz it's a semicircle )
and let § be sigma as my keyboard doesn't have Sigma , Sigma is a kind of Density , it is for those objects in which mass is distributed in area , like this case , It's unit is kg /m²
So let mass of Bigger disc be πr2²§/2 let this be m2
Similarly m1= πr1²§/2
now as the plate is only the area between the two semicircles so we can say that It is actually the total R2 semicircle from which R1 semicircle was substracted ?
First we need to find each of their COM
We know for a semi circular disc , the COM is at 4R /3π
So their individual Com is 4r1/3π
and 4r2/3π let them be c1 and c2 respectively
Now x com = ( assuming that the semicircle is coordinated in such a way it's com will be on x axis ) so x com =
total mass is m2-m1
as we are removing the small disc from the larger , You know the values of m1 , m2 , c1 and c2 , so put them
And just to clear this why are we substracted m1 from m2
cuz m1 is πr1²§/2 and m2 is πr2²§/2
and given that r2>r1 { as r2 is outer radius and r1 is inner radius }so m2>m1
That means it will have area
Let the Bigger radius Disc have Area πr2²/2 (r2 means outer radius and not r* 2) ( why Did I divide by two ? cuz it's a semicircle )
and let § be sigma as my keyboard doesn't have Sigma , Sigma is a kind of Density , it is for those objects in which mass is distributed in area , like this case , It's unit is kg /m²
So let mass of Bigger disc be πr2²§/2 let this be m2
Similarly m1= πr1²§/2
now as the plate is only the area between the two semicircles so we can say that It is actually the total R2 semicircle from which R1 semicircle was substracted ?
First we need to find each of their COM
We know for a semi circular disc , the COM is at 4R /3π
So their individual Com is 4r1/3π
and 4r2/3π let them be c1 and c2 respectively
Now x com = ( assuming that the semicircle is coordinated in such a way it's com will be on x axis ) so x com =
total mass is m2-m1
as we are removing the small disc from the larger , You know the values of m1 , m2 , c1 and c2 , so put them
And just to clear this why are we substracted m1 from m2
cuz m1 is πr1²§/2 and m2 is πr2²§/2
and given that r2>r1 { as r2 is outer radius and r1 is inner radius }so m2>m1
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