$$\text { Find the required quantity given the wire that lies along the curve } r \text { and has density } \delta .$$

question 106

Multiple Choice

$$\text { Find the required quantity given the wire that lies along the curve } r \text { and has density } \delta .$$
-Moment of inertia $\mathrm { I } _ { \mathrm { Z } }$ about the $\mathrm { z }$ -axis, where $\mathbf { r } ( \mathrm { t } ) = ( 5 \cos \mathrm { t } ) \mathbf { i } + ( 5 \sin \mathrm { t } ) \mathbf { j } , 0 \leq \mathrm { t } \leq \frac { \pi } { 2 } ; \delta = 2 ( 1 + \sin 2 \mathrm { t } )$

• A) \(\mathrm { I } _ { \mathrm { Z } } = 10 \left( \frac { \pi + 2 } { 2 } \right)\)
• B) \(\mathrm { I } _ { Z } = 250 \left( \frac { \pi } { 2 } \right)\)
• C) \(\mathrm { I } _ { \mathrm { Z } } = 0\)
• D) \(\mathrm { I } _ { \mathrm { Z } } = 250 \left( \frac { \pi + 2 } { 2 } \right)\)

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Definitions:

Musculoskeletal Accidents

Injuries or traumas that affect muscles, bones, ligaments, or tendons, often resulting from accidents or physical activities.

Indirect Costs

Expenses not directly tied to a specific product or activity, often including overheads like administration, personnel, and security.

Crutches

Supports used by individuals to help transfer weight from the legs to the upper body during walking or standing.

Grasp Arm

A physical action or maneuver used to hold or support someone's arm, often for assistance or stability.