Calculating Center of Gravity After Pizza Cut: A Headache?

[skiboka33]

hi, here's my question...

A pizza has a center of gravity at C, in the middle of the pizza radius = R
A smaller circle of pizza is cut from the pizza of radius R/2 at the left side of the pizza so that one the diameter of the hole where the smaller piece was stretches from the edge of the pizza to the center...

This gives a new center of gravity, C', what is the distance, x, between C' and C...

thanks this question is really givin me headaches...

 

[skiboka33]

and let me know if its confusing... (ps, take the word "one" out in "one the diameter", just a typo, lol, thanks again)

 

[Doc Al]

the old "negative mass" trick :-)

Treat the small pizza as a pizza with negative mass. Then find the center of mass of the two "pizzas" taken together: The normal pizza + the small pizza with negative mass.

 

[Pyrrhus]

You will also need the $\sigma = \frac{mass}{area}$ trick.

 

[skiboka33]

:)

thanks guys i think i got it, didnt know about that negative mass trick!

C' = [(A1)(C) - (A2)(C-R/2) ] / (A1 - A2)

right?

which simplifies to

C' = C + R/6

C' - C = R/6 = Xcm

woot! thanks!