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

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Homework Help Overview

The discussion revolves around calculating the center of mass (CM) for a thin rectangular plate with a circular hole. The plate has a uniform areal density and specific dimensions, while the hole's position and size are also defined. Participants are exploring the implications of these parameters on the calculation of the CM.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are discussing the need to calculate the CM and are considering different methods, including using position vectors for both the plate and the hole. There is also a mention of using the moment of inertia and the principal axis theorem as a potential approach.

Discussion Status

The discussion is active, with participants questioning the starting point for the calculation and exploring various methods to approach the problem. Some guidance has been offered regarding the use of position vectors, but no consensus has been reached on a specific method.

Contextual Notes

Participants have noted the challenge of starting the calculation and the constraints posed by the problem's requirements, including the need to account for the mass of the removed circular disc.

heloudan
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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
 
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do you have to calculate it?
you can hang it from two or more points to find the CM :-)
 
yes i have to calculate it i don't even know where to start
 
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)
 
If you know the moment of inertia at any two points, can you use the principal axis theorem to triangulate the CM?
Bob S
 

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