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MMMU-Pro / validation_Mechanical_Engineering_18 / The disk has a constant angular velocity p about its z-axis, and the yoke A has…

Problem

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question

The disk has a constant angular velocity p about its z-axis, and the yoke A has a constant angular velocity

\omega_{2}

about its shaft as shown. Simultaneously, the entire assembly revolves about the fixed X-axis with a constant angular velocity

\omega_{1}

. Determine the expression for the angular acceleration of the disk as the yoke brings it into the vertical plane in the position shown. Solve by picturing the vector changes in the angular-velocity components.<image 1>

Plain-text mathematical notation (without MathML)

The disk has a constant angular velocity p about its z-axis, and the yoke A has a constant angular velocity ω₂ about its shaft as shown. Simultaneously, the entire assembly revolves about the fixed X-axis with a constant angular velocityω₁. Determine the expression for the angular acceleration of the disk as the yoke brings it into the vertical plane in the position shown. Solve by picturing the vector changes in the angular-velocity components.<image 1>

Original LaTeX notation

The disk has a constant angular velocity p about its z-axis, and the yoke A has a constant angular velocity $\omega_{2}$ about its shaft as shown. Simultaneously, the entire assembly revolves about the fixed X-axis with a constant angular velocity$\omega_{1}$. Determine the expression for the angular acceleration of the disk as the yoke brings it into the vertical plane in the position shown. Solve by picturing the vector changes in the angular-velocity components.<image 1>

img type

Diagrams

options

$\alpha=(pw_{1}i-pw_{2}j+w_{1}w_{2}k)rad/s^{2}$
$\alpha=(pw_{2}i-pw_{1}j+2w_{1}w_{2}k)rad/s^{2}$
$\alpha=(pw_{2}i-pw_{1}j+w_{1}w_{2}k)rad/s^{2}$
$\alpha=(pw_{1}i+pw_{2}j+w_{1}w_{2}k)rad/s^{2}$
$\alpha=(2pw_{2}i-pw_{1}j+w_{1}w_{2}k)rad/s^{2}$
$\alpha=(pw_{2}i-2pw_{1}j+w_{1}w_{2}k)rad/s^{2}$
$\alpha=(pw_{1}i-pw_{2}j-w_{1}w_{2}k)rad/s^{2}$
$\alpha=(pw_{2}i+pw_{1}j-w_{1}w_{2}k)rad/s^{2}$
$\alpha=(pw_{2}i-2pw_{1}j-w_{1}w_{2}k)rad/s^{2}$

subject

Mechanical_Engineering

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Source and history

upstream_id / Original problem ID: validation_Mechanical_Engineering_18
task_id: fbc2d303-76fa-52b8-8f5b-835f83d5ccf1
task_key: standard~20~2810~20options~29--test--validation~5fMechanical~5fEngineering~5f18
task_revision_id: 3
config / split: standard (10 options) / test

Official source

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