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

In summary, the conversation is about a new member asking for help with a physics problem involving finding the distance of the center of mass of a quarter of a disc from the center. The problem is solved using the concept of symmetry and folding, without the use of calculus. The hint given is to consider the shift in center of mass when folding a full circle in half.
  • #1
Ujjawal Kumar
2
0
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.
 
Last edited:
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  • #2
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
  • #3
Yes, and thank you BvU!
 
  • #4
This problem actually took me quite some time to figure...thnx for the hint BvU!
 

1. What is a disc?

A disc is a two-dimensional circular object with a flat surface and a circular edge. It is commonly referred to as a "disk" in computer terminology.

2. What is the center of mass of a disc?

The center of mass of a disc is the point at which the weight of the disc is evenly distributed in all directions. It can be thought of as the balance point of the disc, where it would balance perfectly on a pivot.

3. How is the center of mass of a disc calculated?

The center of mass of a disc can be calculated by finding the average position of all the particles that make up the disc. This can be done by dividing the total mass of the disc by the total area and finding the center of that area.

4. What is the significance of the center of mass in a disc?

The center of mass is important in a disc because it represents the point at which the disc will be in perfect equilibrium. This means that if the disc is suspended from its center of mass, it will not rotate or move in any direction.

5. How does the center of mass affect the motion of a disc?

The center of mass plays a major role in the motion of a disc. If a force is applied to the center of mass, the disc will experience a translational motion. If the force is applied off-center, the disc will also experience a rotational motion around its center of mass.

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