Hi guys,(adsbygoogle = window.adsbygoogle || []).push({});

recently I am reading Kleppner's Mechanics

about center of mass,

well, I am always a fairly fast learner,

but I really got stick here.

you see,

in the page 119

example 3.3 (in short, a rod with nonuniform density )

let Q(x) be the function density of location vector

it said

[tex]M=\int{dm}[/tex]

[tex]\int{dm}=\int{Qdx}[/tex]

however, when I do the calculation on my own.

[tex]dm=Qdx+xdQ[/tex]

then intergrate both sides

[tex]\int{dm}=\int{Qdx}+\int{xdQ}[/tex]

so should there be Int(xdQ) ?

2.) I just out of the blue thinking of during my calculation, what if I come across a vector times itself two times?

as for just one time, then it is a dot product,

but, a scalar simply can't dot product with a vector!!

so what is the meaning of [itex]{v}^3[/itex]? (v is a vector)

Thanks for your reading!!

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# Center of mass and a bit vector calculus

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