Calculating the Center of Mass for an L-Shaped Object

[KiNGGeexD]

Could someone confirm if my method here is correct and if not maybe a few tips
:)
I have an L shape constructed of three "boxes" of side length a what is the centre of mass?I know that CoM= the sum of moments (m*a)/ the sum of masses

So if I split the L into two parts, one box and two boxes! (Treating the two boxes as one beam) It would be fair to say that a= 2a and mass =2m for the longer beam.So...

CoM=2m*2a+ m*a/ 3(m) 2/3*a^2 mI suspect this is incorrect but not sure what to do? Ty

Thanks guys

 

[SteamKing]

You are not making too much sense. Take a moment to take a deep breath.

If this is a homework problem, it is recommended that you follow the template and give us a complete statement of the problem you are trying to solve. For your peace of mind and ours, a sketch would replace a lot of verbal handwaving.

 

[KiNGGeexD]

Ok no problem! I will upload one shortly :)

I know I got a bit ahead of myself

 

[KiNGGeexD]

Ok I have figured my problem out! I was not thinking!

I treated my beams as three point particles as we can do with CoM!

I then defined a co-ordinate system and solved for the x and y components and expressed the CoM I'm coordinate notation I.e (x,y)

Thanks for you help!

 

[HallsofIvy]

The x, y, and z coordinates of the center of mass of the entire figure are the weighted averages of the coordinates of the centers of masses of the individual parts, each weighted by its mass. That's essentially the same as "treating the beams as three point particles" as you say you did.

 

[KiNGGeexD]

Well my problem was only two dimensional so I disregarded the CoM in the z plane :)

 

[KiNGGeexD]

Is this correct however?

 

[KiNGGeexD]

Ok my answer for both the x and y direction because they are symmetrically the same I got 5a/6 which seems reasonable as it would be outside the system :)

 

[KiNGGeexD]

I misspoke (typed) the CoM would be inside the system:)