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The design of the rotating arm OA of a controlmechanism requires that it rotate about
Chapter 7, Problem 7/22(choose chapter or problem)
The design of the rotating arm OA of a control mechanism requires that it rotate about the vertical Z-axis at the constant rate \(\Omega=\dot{\beta}=\pi \mathrm{rad} / \mathrm{s}\). Simultaneously, OA oscillates according to \(\theta=\theta_{0} \sin 4 \Omega t\), where \(\theta_{0}=\pi / 6\) radians and t is in seconds measured from the time when \(\beta=0\). Determine the angular velocity \(\omega\) and the angular acceleration \(\alpha\) of OA for the instant (a) when t = 1/2 s and (b) when t = 1/8 s. The x-y reference axes rotate in the X-Y plane with the angular velocity \(\Omega\).
Questions & Answers
QUESTION:
The design of the rotating arm OA of a control mechanism requires that it rotate about the vertical Z-axis at the constant rate \(\Omega=\dot{\beta}=\pi \mathrm{rad} / \mathrm{s}\). Simultaneously, OA oscillates according to \(\theta=\theta_{0} \sin 4 \Omega t\), where \(\theta_{0}=\pi / 6\) radians and t is in seconds measured from the time when \(\beta=0\). Determine the angular velocity \(\omega\) and the angular acceleration \(\alpha\) of OA for the instant (a) when t = 1/2 s and (b) when t = 1/8 s. The x-y reference axes rotate in the X-Y plane with the angular velocity \(\Omega\).
ANSWER:
Step 1 of 6
Since the rotating arm 
