Find the centre of mass of a semi circular plate

AI Thread Summary
To find the center of mass of a semi-circular plate with a radius R and a linearly varying density from 'd' at the center to '2d' at the circumference, the formula Xcom = (∫xdm)/M is used. The challenge lies in expressing dm in terms of dx, which can be resolved by using polar coordinates for setting up the integrals. Participants discuss the need for clear equations for density and dm as functions of x to facilitate the calculations. Utilizing polar coordinates simplifies the integration process for mass and the first moment. The discussion emphasizes the importance of correctly defining the density function to solve for the center of mass effectively.
Neilquintal
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1. Find the centre of mass of a semi circular plate of radius R, the density of which linearly varies with distance, 'd' at the centre to a value '2d' at the circumference.
2. Xcom = (∫xdm)/M
3. I tried attempting the solution but I am not really knowing how to get dm in terms of dx
 
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Since you have a semi-circular plate, why not use polar coordinates to set up your integrals for the mass and the first moment?
 
Neilquintal said:
1. Find the centre of mass of a semi circular plate of radius R, the density of which linearly varies with distance, 'd' at the centre to a value '2d' at the circumference.




2. Xcom = (∫xdm)/M



3. I tried attempting the solution but I am not really knowing how to get dm in terms of dx
What is your equation for density as a function of x? What is your equation for dm as a function of x?

Chet
 
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