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# A thin wire is bent into the shape of a semicircle $x^2 + y^2 = 4$, $x \geqslant 0$. If the linear density is a constant $k$, find the mass and center of mass of the wire.

## Mass of the wire is 2$\pi k$ Centre of mass of the wire is $$\left(\frac{4}{\pi}, 0\right)$$

Vector Calculus

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##### Lily A.

Johns Hopkins University

##### Kristen K.

University of Michigan - Ann Arbor

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### Video Transcript

so finding the center of mess. This problem Let me explain a setup First. First from the textbook, you can find a former off Mass and center of mass. In case you don't remember, this's the former and does Andi We need a Paramount try harder to do this in the growth we need a parametric sex It was to call society. Why was to society and his ex ex is post now Negative. So it's a dry health off a certain look so that biggest egos from negative pie over to to power too. And we'Ll have to figure out GS which was dx DT Square prostitute y squared Wei have square with force so is two and DT So once we have everything is pretty much just computation Some competition left. So, for example, we compute the master first. That should be t goes from Nephew Pie over to pie over too in this problem that that's it, he's simply okay, So we have Hey, the s is to tt So we got to k times the difference between bunk, which is pie or to pike and this hump you, huh? The center ofthe mess. So the x coordinate is keeping by this. Head X is to co sign T and Ro is K and the esus to TT. So have we, um, pulled for Kay coastline t That should keep us our society. We are one minus nifty once. So is too on similarities This artist's X coordinate And why coordinate is this? You're droll? Ah, why should be to sign He and roll is okay. Yes is he? And similarly we have thiss I have signed it. So your nephew of course I NT we still have four k over and never co signed the forms here to here. But they they're both zero. What? They're both here. So their difference should be sure he's here. So? So the mess should be Should be two pi k in the center ofthe masses we compute. It should be hate kay over him And the wild card they should be zero has to make sense is symmetric with respect. Except this is a right hell Part of the circle. Sorry, I haven't feel so em is to Pike. So we should replace this by to Pike and Dash B four over Pi We should use this number

#### Topics

Vector Calculus

##### Lily A.

Johns Hopkins University

##### Kristen K.

University of Michigan - Ann Arbor

Lectures

Join Bootcamp