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When finding the center of mass of curved objects(hemisphere,ring etc.) how do we know the limits of the angle to be used in the integral?

When finding the center of mass of curved objects(hemisphere,ring etc.) how do we know the limits of the angle to be used in the integral? 

Grade:11

1 Answers

Yash Baheti IIT Roorkee
askIITians Faculty 97 Points
7 years ago
Hi,

The angle to take depends upon the small element taht you have taken to integrate.
Take a case of a ring. If we take a small d(theta) element and mass corresponding to it on circumfrence than that d(theta) has to be integrate from 0 ( that is ur starting point ) to 2pi ( which is full cicrle). In this way ull will be considering all the mass lying on the circumfrence.

Sinilarly when we take a sphere, the small element we take is a very thin hollow speher and here we integrate its width.

When we do it for a hollow sphere, we take a ring at any place and we find find its radius using the angle it is substending at centre. So here the theta will vary from -pi/2 to pi/2.

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