Math Is Fun Forum

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Center of mass of general figures.

What would be the center of mass of the following figures? How to determine so?

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Center of mass of general figures.

In each case, take the centre of mass of each individual stick, then take the average of those.

eg. In c), take (0,0) to be the point where the two sticks meet.
Then their centres of mass are at (L/2,0) and (0,L/2).
The centre of mass of the overall shape is therefore (L/4,L/4).

b) is similar, but there's an additional stick involved with a CoM at (L,L/2).
This figure has an overall CoM at (L/2,L/3).

a) and d) are perhaps a bit trickier, but they're still solved in much the same way.

You can sometimes simplify things by symmetry arguments.
a), b) and d) all have vertical lines of symmetry, so it's clear that the CoM will lie somewhere on it.
In fact, d) has 3 lines of symmetry so finding their intersection point will be enough to solve that one.

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Why did the vector cross the road?
It wanted to be normal.