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The disk is moving to the left such that it has an angular acceleration a = 14 rad/s² and angular velocity w = 3 rad/s at the instant shown. (Figure 1) Figure L B 30° 0.5 m w, a D 450 1 of 1 Part A If it does not slip at A, determine the acceleration of point B. Enter the x and y components of the acceleration separated by a comma. (aB)z, (aB)y= Submit Provide Feedback |Π| ΑΣΦ 11 | vec Request Answer ? m/s²

The disk is moving to the left such that it has an angular acceleration a = 14 rad/s² and angular velocity w = 3 rad/s at the instant shown. (Figure 1) Figure L B 30° 0.5 m w, a D 450 1 of 1 Part A If it does not slip at A, determine the acceleration of point B. Enter the x and y components of the acceleration separated by a comma. (aB)z, (aB)y= Submit Provide Feedback |Π| ΑΣΦ 11 | vec Request Answer ? m/s²

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### Understanding Angular Motion of a Disk #### Problem Statement: The problem involves determining the acceleration of point \( B \) on a disk that is moving to the left. At the given instant, the disk has an angular acceleration \(\alpha = 14 \, \text{rad/s}^2\) and an angular velocity \(\omega = 3 \, \text{rad/s}\). #### Objective: To determine the acceleration of point \( B \) under the given conditions. #### Instructions: 1. **Visualizing the Disk:** - Observe the diagram of the disk provided. - The disk is rotating clockwise as shown by the arrow indicating \(\omega\) and \(\alpha\). - Note the specific angles provided and the geometry of the disk, which bears a radius of \(0.5 \, \text{m}\). 2. **Diagram Explanation:** - The figure displays a right-angled triangle inscribed in the circle formed by two radii and a chord. - Point \( A \) is at the base of the disk where it contacts the ground. - Points and angles on the disk are marked as follows: - Point \( C \) is the center. - Point \( B \) is to the left of the center, \(0.5 \, \text{m}\) from \(C\), at an angle of \(30^\circ\) to the horizontal. - Point \( D \) is above the center \(C\), \(0.5 \, \text{m}\) from \(C\), at an angle of \(45^\circ\). 3. **User Task:** - Calculate the x and y components of the acceleration of point \( B \). - Input your answers in the specified format: \((a_B)_x, (a_B)_y\). #### Solution Steps: 1. **Identify Known Values:** - Angular acceleration \(\alpha = 14 \, \text{rad/s}^2\) - Angular velocity \(\omega = 3 \, \text{rad/s}\) - Radius \( r = 0.5 \, \text{m} \) 2. **Application of Kinematic Equations for Rotational Motion:** - Utilize the equations for linear acceleration derived from angular motion: \[ a = r \alpha \
Transcribed Image Text:### Understanding Angular Motion of a Disk #### Problem Statement: The problem involves determining the acceleration of point \( B \) on a disk that is moving to the left. At the given instant, the disk has an angular acceleration \(\alpha = 14 \, \text{rad/s}^2\) and an angular velocity \(\omega = 3 \, \text{rad/s}\). #### Objective: To determine the acceleration of point \( B \) under the given conditions. #### Instructions: 1. **Visualizing the Disk:** - Observe the diagram of the disk provided. - The disk is rotating clockwise as shown by the arrow indicating \(\omega\) and \(\alpha\). - Note the specific angles provided and the geometry of the disk, which bears a radius of \(0.5 \, \text{m}\). 2. **Diagram Explanation:** - The figure displays a right-angled triangle inscribed in the circle formed by two radii and a chord. - Point \( A \) is at the base of the disk where it contacts the ground. - Points and angles on the disk are marked as follows: - Point \( C \) is the center. - Point \( B \) is to the left of the center, \(0.5 \, \text{m}\) from \(C\), at an angle of \(30^\circ\) to the horizontal. - Point \( D \) is above the center \(C\), \(0.5 \, \text{m}\) from \(C\), at an angle of \(45^\circ\). 3. **User Task:** - Calculate the x and y components of the acceleration of point \( B \). - Input your answers in the specified format: \((a_B)_x, (a_B)_y\). #### Solution Steps: 1. **Identify Known Values:** - Angular acceleration \(\alpha = 14 \, \text{rad/s}^2\) - Angular velocity \(\omega = 3 \, \text{rad/s}\) - Radius \( r = 0.5 \, \text{m} \) 2. **Application of Kinematic Equations for Rotational Motion:** - Utilize the equations for linear acceleration derived from angular motion: \[ a = r \alpha \
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