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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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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