You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.
system
<image>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>
A. $\alpha=(pw_{1}i-pw_{2}j+w_{1}w_{2}k)rad/s^{2}$
B. $\alpha=(pw_{2}i-pw_{1}j+w_{1}w_{2}k)rad/s^{2}$
C. $\alpha=(pw_{2}i-2pw_{1}j+w_{1}w_{2}k)rad/s^{2}$

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
user
B
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>
A. $\alpha=(pw_{1}i-pw_{2}j+w_{1}w_{2}k)rad/s^{2}$
B. $\alpha=(pw_{2}i-pw_{1}j+w_{1}w_{2}k)rad/s^{2}$
C. $\alpha=(pw_{2}i-2pw_{1}j+w_{1}w_{2}k)rad/s^{2}$

Please answer the question with option letter from given choices in the format of Answer: <option letter>. You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
val