Center of Mass Question?

Question

How do you find the center of mass of a "T" shape.
Let's say there are two rods m1 and m2 with the same length L.
They are joined together to form a "T" shape (no overlaps).

Any Ideas?

Answer 1

Suppose the coordinates of the ends of rod1 are (0,0) and (L,0)

And the ends of rod 2 are (L,L/2) and (L,-L/2).



Draw a clear diagram so you can see what is going on.



By symmetry, the centre of mass lies on the x axis. Suppose its coordinates are (X,0). Mark this on your diagram.



Take moments about a convenient point, e.g the origin.

The moment due to the combined mass acting at (X,0) must equal the sum of the separate moments.



(m1+m2)X = m1(L/2) + m2L

= L(m1/2 + m2)

= L(m1 + 2m2)/2



X= L(m1 + 2m2)/(2(m1 + m2))

Answer 2

I guesss other people will know better. but from what I know, If this question is practical - youll have to join both M1 & M2. then youll have to hang them from one point (any point, preferably any middle point) by an inextensible string. then you mark out (i.e. draw a line) where the string crosses the part of the rod. Then do the same thing from another point and mark. The point in the mechanism (the joined rods) where both the marks intersect is the center of mass of it.



Hope it helps.

Answer 3

Well, if you look at it like a "T," then by symmetry you know it has to be along the center line of the "T." In short, you take the moments of both rods and find the y-value where the sum of the moments is equal to zero.



In long, if the origin of the graph is at the base of the "T," follow these four steps:

1) Find the center of mass of each rod.

2) Find the total mass of each rod (which may be given)

3) Sum the moments of the rods. This means to multiply the mass of each rod by the distance each rod's center of mass is from a specified point. Specifically, to find the moment of one rod along the y-axis, multiply the mass by the y-value of a point, minus the y-value of the rod's center of mass. Do this to both rods, and sum the results. In a formula, it would look like this:



Total Moment = A(y - c) + B(y - d)



where:

A = Mass of rod 1

B = Mass of rod 2

c = y-value of the center of mass of rod 1

d = y-value of the center of mass of rod 2



4) Find the y-value where Total Moment equals zero. This will give you the center of mass of the "T" shape.



Judging by the additional details, it looks like your y-values are in terms of length. I'm too lazy to reverse-engineer your question from the additional details, but my method should still work using the "L" variable in the y-value.

Answer 4

I'm just going to take a wild guess here:



Find the center of each of the rods and the mid point of the line that connects those two centers is the center of mass.

Answer 5

the middle of mass calculations is extremely useful for the NASA people whilst they are launching rockets and load from a rocket, like a probe. yet another useful utility is determining the shy away of a gun, or the different hearth weapon, whilst one shoots with it. actually, it somewhat is useful for any technique wherein an merchandise turns itself in its opposite numbers and the size of its opposite numbers are comparable with the preliminary merchandise. you spot, whilst an merchandise blows up, or in simple terms turns itself in its opposite numbers, and it somewhat is shifting with a persevering with velocity, the middle of mass of that merchandise retains shifting with the comparable velocity, despite if the opposite numbers do no longer guard the flow till now the explosion and despite if the middle of mass does not have a actual help (think of on the middle of mass of a ring or of a triangle). subsequently, you may administration the path of the bullet, case in point, whilst he/she shoots. whilst one fires a gun, by using adjustments in hundreds between the gun and the bullet, the bullet is going out with a severe velocity, jointly as the gun has a small velocity, such that the M*V=m*v, the place the capitals are the mass (M) and the fee (V) of the gun and the small letters are the mass (m) and the fee (v) of the bullet. this is the reason you are able to nonetheless nonetheless carry a gun in his hand with out being thrown at a number of metres remote from the placement he/she has fired. And the middle of mass remains nonetheless subsequently, because of the fact the gun wasn't walking around whilst it grew to become into fired. desire this facilitates.

Answer 6

If they are the same weight, it's the midpoint of the line joining the centers of the two rods. If they are not the same weight, take the weighted average of their midpoints.