Axle 600 rpm FIGURE P8.37 37. What is the angular momentum about the axle of the 2.0 kg, 4.0-cm-diameter rotating disk in Figure P8.37?

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**Problem 37:**

What is the angular momentum about the axle of the 2.0 kg, 4.0-cm-diameter rotating disk in Figure P8.37?

**Figure P8.37 Explanation:**

The diagram shows a disk with an axle at its center. The disk is rotating at a speed of 600 revolutions per minute (rpm). The axle is marked, and an arrow indicates the direction of rotation.

To find the angular momentum (\(L\)) of the disk, use the formula:

\[ L = I \cdot \omega \]

where \(I\) is the moment of inertia and \(\omega\) is the angular velocity in radians per second.

**Step 1: Calculate the moment of inertia (\(I\))**  
For a solid disk:  
\[ I = \frac{1}{2} m r^2 \]  
where \(m = 2.0 \, \text{kg}\) and \(r = \frac{4.0 \, \text{cm}}{2} = 0.02 \, \text{m}\).

**Step 2: Convert angular velocity (\(\omega\)) to radians per second**  
\[ 600 \, \text{rpm} = 600 \times \frac{2\pi \, \text{rad}}{60 \, \text{s}} = 20\pi \, \text{rad/s} \]

**Step 3: Calculate angular momentum (\(L\))**  
Using the values from above, calculate \(L\).

Insert the values to solve the problem on an educational platform or class setting.
Transcribed Image Text:**Problem 37:** What is the angular momentum about the axle of the 2.0 kg, 4.0-cm-diameter rotating disk in Figure P8.37? **Figure P8.37 Explanation:** The diagram shows a disk with an axle at its center. The disk is rotating at a speed of 600 revolutions per minute (rpm). The axle is marked, and an arrow indicates the direction of rotation. To find the angular momentum (\(L\)) of the disk, use the formula: \[ L = I \cdot \omega \] where \(I\) is the moment of inertia and \(\omega\) is the angular velocity in radians per second. **Step 1: Calculate the moment of inertia (\(I\))** For a solid disk: \[ I = \frac{1}{2} m r^2 \] where \(m = 2.0 \, \text{kg}\) and \(r = \frac{4.0 \, \text{cm}}{2} = 0.02 \, \text{m}\). **Step 2: Convert angular velocity (\(\omega\)) to radians per second** \[ 600 \, \text{rpm} = 600 \times \frac{2\pi \, \text{rad}}{60 \, \text{s}} = 20\pi \, \text{rad/s} \] **Step 3: Calculate angular momentum (\(L\))** Using the values from above, calculate \(L\). Insert the values to solve the problem on an educational platform or class setting.
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