Center of mass

1. Mar 14, 2014

Aliasa

1. The problem statement, all variables and given/known data

Find the center of mass of a uniform sheet in the form of a circular disc
with a hole bounded by the equations x^2 + y^2 ≤ 1 and (x - 1/2)^2 + y^2 ≥ (1/16).

2. Relevant equations

3. The attempt at a solution

2. Mar 14, 2014

SteamKing

Staff Emeritus
Can you find the area of the figure?

3. Mar 14, 2014

Aliasa

That is all the info given.

4. Mar 14, 2014

Staff: Mentor

Hi Aliasa. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif [Broken]

Using your knowledge of mathematics, sketch the shape. Then post it here.

Last edited by a moderator: May 6, 2017
5. Mar 14, 2014

HallsofIvy

Staff Emeritus
Yes, but can you find the area? This is a disk with a hole in it. It would be a good idea to at least draw a picture of the "hole bounded by the equations x^2 + y^2 ≤ 1 and (x - 1/2)^2 + y^2 ≥ (1/16)." Those boundaries are circles. Can you graph the circles?

6. Mar 14, 2014

Staff: Mentor

Where is the center of mass of the outer circle located?
Where is the "center of mass" of the hole located?
What is the area of the outer circle?
What is the area of the hole?

7. Mar 15, 2014

Aliasa

It turns out the question is horribly worded. The sheet is bounded by the former equation, while hole by the latter -_-. Since the equations are inequality, by taking density into account, I feel the center of mass should be a range too. The hole can have a max radius of .5, sheet, 1. Hole can have a min radius of 1/4, when the sheet can have a minimum of 3/4.

8. Mar 15, 2014

Staff: Mentor

You are misunderstanding the question. The metal template is very precisely defined by the two equations; there is no range of possible shapes and sizes. The centre of mass is an exact point. The two equations together define the metal surface, the hole is where there is metal missing.

Have you sketched the shape yet?

9. Mar 15, 2014

Aliasa

If that is the case then the question is trivial. I have solved it if those equations represent what you say. But doing that only takes me 5 minutes or less, which I can't understand. All the other questions on the assignment take in excess of 3 hours.

10. Mar 15, 2014

Aliasa

11. Mar 15, 2014

SteamKing

Staff Emeritus
That's pretty astounding. Can you provide an example of one of these 3-hour problems?

12. Mar 15, 2014

Staff: Mentor

Yes. That's correct. Nice job.

Chet

13. Mar 15, 2014

Aliasa

This is one of those questions. Others seem easy now that I have done them. Yet to start on this one. The astounding thing is there's no mention of 'coefficient of restitution' in lecture notes.

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