How Do You Calculate the Center of Mass for a Plate with a Circular Hole?

[heloudan]

A thin rectangular plate of uniform areal density σ = 3.13 kg/m2 has length of 44.0 cm and width of 26.0 cm. The lower left hand corner is located at the origin, (x,y)= (0,0) and the length is along the x-axis.
There is a circular hole of radius 7.00 cm with center at (x,y) = (16.00,11.00) cm in the plate

Calculate the x-coordinate of CM of the plate.!?
Calculate the distance of the plate's CM from the origin.!?


for some odd reason i can figure out any other problem but this one if someone could help me out that would be great

 

[Molydood]

do you have to calculate it?
you can hang it from two or more points to find the CM :-)

 

[heloudan]

yes i have to calculate it i don't even know where to start

 

[rl.bhat]

Find the position vectors of the CM of rectangular plate and removed circular disc.
Let M be the mass of plate and m be the mass of the disc.
Position vector R1 of M = (022i + 0.13j). Mass M = σ*A. where A is the area of the plate
Position vector R2 of m = (0.16i + 0.11j) Mass n = σ*a ,where a is the area of the removed circular disc.
Then the position vector of CM of the remaining mass of the rectangular plate is
R = (M*R1 - m*R2)/(M - m)

 

[Bob S]

If you know the moment of inertia at any two points, can you use the principal axis theorem to triangulate the CM?
Bob S