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

[Ujjawal Kumar]

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 ……………………….

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.

 

[BvU]

Hello Ujjawal, welcome to PF !

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 ?

 

[Ujjawal Kumar]

Yes, and thank you BvU!

 

[AR1399]

This problem actually took me quite some time to figure...thnx for the hint BvU!