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### Moment of inertia of wire hoop A circular wire ho…

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YZ
University of Illinois at Urbana-Champaign
Problem 36

# Center of mass of wire with variable density Find the center of mass of a thin wire lying along the curve $\mathbf{r}(t)=t \mathbf{i}+2 t \mathbf{j}+$ $(2 / 3) t^{3 / 2} \mathbf{k}, 0 \leq t \leq 2,$ if the density is $\delta=3 \sqrt{5}+t$

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## Video Transcript

no handle or eagles to t to t 2/3 comes t to the three f's 41 0 to 2. So now the derivative Ask the marshal swear with one plus four plus t which is t plus five. What? So the mess will be this Is he on the line? It's rule which is 0 to 2, three times why plus t did see which is 36 and for a TSH first moments and we have and was he is extra zero tips Tell Adi s and I see is why Timestony s oversee and I'm that's wise Z come study s oversee. It's uploading the data We have 38 76 in one 44 was seven times for two respectively. So now we know this is a mass equals two And this, um c y over and em if x c over m and Abbott X Y over and was just equal to formula data unseen over. It's in unseen over noni and, uh, for transport yourself. That's it

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