Finding Center of Mass of Disc with Hole

[Aliasa]

Homework Statement

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).

Homework Equations

The Attempt at a Solution

 

[SteamKing]

Can you find the area of the figure?

 

[Aliasa]

That is all the info given.

 

[NascentOxygen]

That is all the info given.

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

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

 

[HallsofIvy]

Can you find the area of the figure?

That is all the info given.

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?

 

[Chestermiller]

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?

 

[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.

 

[NascentOxygen]

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.

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?

 

[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.

 

[Aliasa]

The answer is (-1/30,0) btw.

 

[SteamKing]

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.

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

 

[Chestermiller]

The answer is (-1/30,0) btw.

Yes. That's correct. Nice job.

Chet

 

[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.