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YZ

# Center of mass and moments of inertia for wire with variable density Find the center of mass and the moments of inertia about the coordinate axes of a thin wire lying along the curve$$\mathbf { r } ( t ) = t \mathbf { i } + \frac { 2 \sqrt { 2 } } { 3 } t ^ { 3 / 2 } \mathbf { j } + \frac { t ^ { 2 } } { 2 } \mathbf { k } , \quad 0 \leq t \leq 2$$if the density is $\delta = 1 / ( t + 1 )$

## $=\frac{56}{9}$

Integrals

Vectors

Vector Functions

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Johns Hopkins University

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University of Michigan - Ann Arbor

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Idaho State University

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### Video Transcript

job or has the co ordinates t to swerve through over three t three halfs and half of STI square 40 from zero to chew. Oh, it calculates the module off the derivative. We're gonna have one plus team. So there's the mess. Is Dona the S L C which is for the valley in there too? One d t. So, which is to explore is and was he over M So 1/2 terms x don't B s. We'll see which is equals to one. And why Boer is why x z over and 1/2 times Why did he s c when she's too thers? Z bore is, um that's why over now equals to one have tons Zito, the S and C, which is 230 to 45. So that's the sense of mass. And for the movements of inertia, we have ice of X equals two x squared. Sorry. Westward plus thesis Weird, don't it? Yes. Which is given by, um, the answers, but you're was three and, uh, ice. The why is extorted plus thes where DVDs which is you close to 60 64. 15. And I said xe is ex worthless voice word. The other the s to the sixth Woman night recall over Sealift Mass is one succeed or team and to over three. That's it.

YZ
University of Illinois at Urbana-Champaign

#### Topics

Integrals

Vectors

Vector Functions

##### Lily A.

Johns Hopkins University

##### Kristen K.

University of Michigan - Ann Arbor

##### Michael J.

Idaho State University

Lectures

Join Bootcamp