You are looking down on a disc that is spinning counterclockwise in the xy plane (positive z points out of the page towards you). The mass of the disc is 0.5 kg and it has a radius of 0.1 meters. The disc has an angular speed of 45 rotations per minute.

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**Title: Calculating Angular Momentum of a Spinning Disc**

**Description:**

You are observing a disc from above, spinning counterclockwise in the xy plane, where the positive z-axis points out of the page towards you. This disc has a mass of 0.5 kg and a radius of 0.1 meters. It rotates at an angular speed of 45 rotations per minute.

**Diagram:**

The diagram depicts a circle representing the disc oriented in the xy coordinate system. The x and y axes intersect at the center of the circle, suggesting a top-down view of the disk.

**Task:**

Write the angular momentum for this spinning disc in vector form and in units of kg m²/s.

**Solution Steps:**

1. **Convert Rotational Speed to Standard Units:**
   - Given angular speed: 45 rotations per minute.
   - Convert to radians per second: \( \omega = 45 \times \frac{2\pi \text{ radians}}{60 \text{ seconds}} \).

2. **Calculate Moment of Inertia (I):**
   - For a disc, \( I = \frac{1}{2} m r^2 \).
   - \( I = \frac{1}{2} \times 0.5 \, \text{kg} \times (0.1 \, \text{m})^2 \).

3. **Calculate Angular Momentum (L):**
   - \( L = I \omega \).
   - Determine the direction using the right-hand rule (out of the page in the positive z direction).

**Final Answer:**
Represent the angular momentum vector in kg m²/s.
Transcribed Image Text:**Title: Calculating Angular Momentum of a Spinning Disc** **Description:** You are observing a disc from above, spinning counterclockwise in the xy plane, where the positive z-axis points out of the page towards you. This disc has a mass of 0.5 kg and a radius of 0.1 meters. It rotates at an angular speed of 45 rotations per minute. **Diagram:** The diagram depicts a circle representing the disc oriented in the xy coordinate system. The x and y axes intersect at the center of the circle, suggesting a top-down view of the disk. **Task:** Write the angular momentum for this spinning disc in vector form and in units of kg m²/s. **Solution Steps:** 1. **Convert Rotational Speed to Standard Units:** - Given angular speed: 45 rotations per minute. - Convert to radians per second: \( \omega = 45 \times \frac{2\pi \text{ radians}}{60 \text{ seconds}} \). 2. **Calculate Moment of Inertia (I):** - For a disc, \( I = \frac{1}{2} m r^2 \). - \( I = \frac{1}{2} \times 0.5 \, \text{kg} \times (0.1 \, \text{m})^2 \). 3. **Calculate Angular Momentum (L):** - \( L = I \omega \). - Determine the direction using the right-hand rule (out of the page in the positive z direction). **Final Answer:** Represent the angular momentum vector in kg m²/s.
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