## Step : Understanding the Problem - The plate is rotating around the **z-axis**. - The hinge attached is rotating around the **–y axis**. - The link is pointing along the **+x axis**. - We are asked about the **rotational acceleration** of point B (the end of the link), specifically the directions of the components of \(\vec{a}_B\). ### Explanation - **Rotational acceleration** at a point due to angular acceleration \(\vec{\alpha}\) is given by: \(\vec{a}_B = \vec{\alpha} \times \vec{r}_{B/A}\) - **Point B** is at a distance along the +x direction from A. - The **angular acceleration** is around the **–y axis**. ## Step 2: Determining the Direction - **\(\vec{\alpha}\)**: Since the rotation is around the **–y axis**, \(\vec{\alpha}\) points in the **–y direction**. - **\(\vec{r}_{B/A}\)**: This is the position vector from A to B, which is in the **+x direction**. Now, calculate the cross product: - \(\vec{a}_B = \vec{\alpha} \times \vec{r}_{B/A} = (-\hat{y}) \times (+\hat{x})\) From the right-hand rule: - \( \hat{y} \times \hat{x} = -\hat{z} \) - So, \( -\hat{y} \times \hat{x} = -(-\hat{z}) = +\hat{z} \) ### Explanation - The acceleration component at B due to the rotational acceleration is in the **+z direction**. --- ## **Final Answer** - The correct direction for the acceleration of point B is: **[+] z** --- ### **Summary Table** | Direction | Select? | Reason | |-----------|---------|--------------------------------------------------| | +x | No | Not in cross product result | | –x | No | Not in cross product result | | +y | No | Not in cross product result | | –y | No | Not in cross product result | | +z | **Yes** | Result of the cross product | | –z | No | Opposite of the result | | Not accel.| No | Point B is accelerating due to rotation |