How to determine the center of mass of an object?

This is the centroid formula of any dimension, ri vector.

1 dimension, the integral formula that the landlord wants to know can be written as

Xm=f(pdr*r)/m total? (F refers to the integer symbol. In fact, a bar in the middle of F has to be removed, so I can't type it out; P refers to linear density, because it is 1 dimension, so only linear density exists; R refers to the vector position of each point on the object, m always refers to the total mass of the object, and m can also be expressed as f(pdr) by integral.

For example, a pole with uniform quality has the same density everywhere, and it is all P.

xm=f(pdr*r)/(pr)

= 1/2*pr square /(pr)

= 1/2*r

That is, at the center of the pole

If the poles are uneven and belong to the top-heavy type, then the density of each place is p=kr, that is, the foot density is small and the head density is large, which is directly proportional.

Then xm=f(krdr*r)/f(krdr)

=( 1/3*kr cube) /( 1/2*kr square)

=2/3*r

That is, two-thirds of the distance from the foot.