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**Transcription for Educational Website:**

The figure below depicts a camshaft assembly such as one that might be found in an automobile engine to open and close intake and exhaust valves. The cam is a circular disk of radius \( R \) with a hole of diameter \( R \) cut through it. As shown in the figure, the hole does not pass through the center of the disk. The cam with the hole cut out has mass \( M \). The cam is mounted on a uniform, solid, cylindrical shaft of diameter \( R \) and also of mass \( M \). What is the kinetic energy of the entire camshaft assembly when it is rotating with angular speed \( \omega \) about the shaft's axis? (Use any variable or symbol stated above as necessary.)

\[ K = \square \]

**Explanation of the Diagram:**

- The left side of the figure shows a perspective view of the camshaft assembly, consisting of a cylindrical shaft with the cam disk mounted on it. The disk has an off-center hole.
  
- The right side of the figure offers a frontal view of the cam disk. It illustrates the circular disk with a hole, showing the dimensions: the disk radius as \( R \) and the diameter of the hole as \( R \). The non-central position of the hole is highlighted.

This diagram helps visualize the setup for calculating the kinetic energy of the rotating assembly.
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Transcribed Image Text:**Transcription for Educational Website:** The figure below depicts a camshaft assembly such as one that might be found in an automobile engine to open and close intake and exhaust valves. The cam is a circular disk of radius \( R \) with a hole of diameter \( R \) cut through it. As shown in the figure, the hole does not pass through the center of the disk. The cam with the hole cut out has mass \( M \). The cam is mounted on a uniform, solid, cylindrical shaft of diameter \( R \) and also of mass \( M \). What is the kinetic energy of the entire camshaft assembly when it is rotating with angular speed \( \omega \) about the shaft's axis? (Use any variable or symbol stated above as necessary.) \[ K = \square \] **Explanation of the Diagram:** - The left side of the figure shows a perspective view of the camshaft assembly, consisting of a cylindrical shaft with the cam disk mounted on it. The disk has an off-center hole. - The right side of the figure offers a frontal view of the cam disk. It illustrates the circular disk with a hole, showing the dimensions: the disk radius as \( R \) and the diameter of the hole as \( R \). The non-central position of the hole is highlighted. This diagram helps visualize the setup for calculating the kinetic energy of the rotating assembly.
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