Finding the Center of Mass of a Uniform Disc: A Non-Calculus Approach

AI Thread Summary
The discussion focuses on finding the center of mass of one-fourth of a uniform disc without using calculus. A member expresses difficulty in solving the problem, which involves understanding the shift in the center of mass when a full circle is folded in half. Another participant suggests considering symmetry as a key approach to the solution. The hint provided helps the original poster make progress in solving the problem. The conversation emphasizes the importance of geometric reasoning in physics problems.
Ujjawal Kumar
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Hi New member here!
1. Homework Statement

In the figure one-fourth part of a uniform disc of radius R is shown. The distance of the center of mass of this object from center ‘O’ is ……………………….
PictureR.png


Given: For a semi-circular disc with origin of co- ordinate system at the center of circle, the coordinate of its center of mass is (0,4R/3π ).

(Solve this problem without using calculus)

The Attempt at a Solution


I tried for hours but could not find a solution without using calculus.
 
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Hello Ujjawal, welcome to PF :smile: !

A challenging exercise. Think symmetry and folding:
The given information tells you the center of mass shifts from 0 to ##(0,{4\pi \over 3r})## when you fold a full circle in half.

Is that enough of a hint ?
 
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Likes Ujjawal Kumar and SammyS
Yes, and thank you BvU!
 
This problem actually took me quite some time to figure...thnx for the hint BvU!
 

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