Uniform circular disk of radius

In summary, the conversation is about proving that the center of mass of a uniform circular disk with radius R is located at a point (4/3pi)R from the center of the circle. The participants discuss different approaches and seem to question the validity of the problem.
  • #1
johnnyb
14
0
Any help would be great

Show that the centre of the mass of a uniform circular disk of radius, R, is at a point (4/3pi)R from the centre of the circle.
 
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  • #2
The center of mass of a uniform disk is the center.
 
  • #3
Yeh that's what I'm having a problem with, seems like a stupid question, but still have to prove that it is (4/3pi)R
 
  • #4
johnnyb said:
Any help would be great

Show that the centre of the mass of a uniform circular disk of radius, R, is at a point (4/3pi)R from the centre of the circle.
Where is the circle located?
 
  • #5
Thats all the information that is given

Show that the centre of the mass of a uniform circular disk of radius, R, is at a point (4/3pi)R from the centre of the circle

Altho below it does say...

X co-ord is obvious..to find y co-ord integrate using

Mr = [tex]\int[/tex]rdm

and transform y into an appropriate co-ord system
 
  • #6
any ideas?
 
  • #7
that doesn't make sense. i don't know what to tell you.
 
  • #8
Don't worry bout it, i'll keep trying
 
  • #9
In the way it's formulated,the problem's incorrect.It would have made it interesting,if it had mentioned about a half of the initial disk.

Daniel.
 
  • #10
This is nonsense.

The centre of mass of a circular disc with radius 1 unit is going to be 4.19 units from the centre of the disc?


I'd like to see that!
(I could make an end table for my desk that floats in mid-air!)
 

1. What is a uniform circular disk of radius?

A uniform circular disk of radius is a type of geometric shape that has a circular outline and a constant radius. It is often used to model objects such as coins, wheels, and frisbees.

2. How is the radius of a uniform circular disk measured?

The radius of a uniform circular disk can be measured by finding the distance from the center of the disk to its outer edge. This can be done using a ruler, caliper, or other measuring tool.

3. What are the properties of a uniform circular disk?

A uniform circular disk has several properties, including a constant radius, a circular shape, and a uniform mass density. It also has a moment of inertia, which determines its resistance to changes in rotational motion.

4. How is the moment of inertia calculated for a uniform circular disk?

The moment of inertia for a uniform circular disk can be calculated using the formula I = (1/2) * m * r^2, where m is the mass of the disk and r is the radius. This formula assumes that the disk has a constant mass density.

5. What are some real-life applications of a uniform circular disk of radius?

A uniform circular disk of radius has many practical applications, such as in the design of car wheels, bicycle tires, and record players. It is also commonly used in physics experiments to study rotational motion and calculate moments of inertia.

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