The end of a string wrapped around a disk of mass M and radius R is held stationary while the disk falls and unwinds the string. The disk has a center-of-mass moment of inertia I= ½MR2. Using the sketch for reference, what direction is the angular acceleration a of the disk while it is falling? end held B) fixed gravity disk E) a|=0, so the direction is ambiguous M, R string

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The problem involves a disk of mass \( M \) and radius \( R \) with a string wrapped around it. The disk is initially held stationary, while the other end of the string is fixed. The disk has a center-of-mass moment of inertia \( I = \frac{1}{2}MR^2 \). The goal is to determine the direction of the angular acceleration \( \alpha \) of the disk as it falls and unwinds the string.

Options for the direction of \( \alpha \) are provided:
- **A)** Counterclockwise
- **B)** Downward
- **C)** Clockwise (This option is marked as correct)
- **D)** No net angular response
- **E)** The magnitude of \( \alpha \) is zero, so the direction is ambiguous.

**Diagram Explanation:**
The diagram shows the disk with:
- A string wrapped around it.
- An arrow labeled "string" indicating the part of the string leading to the fixed end.
- An arrow indicating the direction of gravity acting downward.
- The disk is labeled with its mass \( M \) and radius \( R \).

The correct answer **(C)** indicates that as the disk falls and unwinds, its angular acceleration is clockwise.
Transcribed Image Text:The problem involves a disk of mass \( M \) and radius \( R \) with a string wrapped around it. The disk is initially held stationary, while the other end of the string is fixed. The disk has a center-of-mass moment of inertia \( I = \frac{1}{2}MR^2 \). The goal is to determine the direction of the angular acceleration \( \alpha \) of the disk as it falls and unwinds the string. Options for the direction of \( \alpha \) are provided: - **A)** Counterclockwise - **B)** Downward - **C)** Clockwise (This option is marked as correct) - **D)** No net angular response - **E)** The magnitude of \( \alpha \) is zero, so the direction is ambiguous. **Diagram Explanation:** The diagram shows the disk with: - A string wrapped around it. - An arrow labeled "string" indicating the part of the string leading to the fixed end. - An arrow indicating the direction of gravity acting downward. - The disk is labeled with its mass \( M \) and radius \( R \). The correct answer **(C)** indicates that as the disk falls and unwinds, its angular acceleration is clockwise.
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