A 0.02-kg top spins in a circle 10.2 cm wide. The linear velocity of the top is 2.41 m/s and it leans at an angle of 87.7°. What is the angular momentum of the top?

To calculate the angular momentum (\(L\)) of the top, we can use the formula:

\[
L = m \cdot v \cdot r
\]

where:
- \(m\) is the mass of the top,
- \(v\) is the linear velocity,
- \(r\) is the radius of the circular path.

### Given:
- Mass \(m = 0.02 \, \text{kg}\)
- Linear velocity \(v = 2.41 \, \text{m/s}\)
- Diameter of the circle = 10.2 cm = 0.102 m, thus the radius \(r = \frac{0.102}{2} = 0.051 \, \text{m}\)

### Calculation:
Now we can plug in the values:

\[
L = 0.02 \, \text{kg} \cdot 2.41 \, \text{m/s} \cdot 0.051 \, \text{m}
\]

Calculating this:

\[
L = 0.02 \cdot 2.41 \cdot 0.051
\]
\[
L = 0.00244842 \, \text{kg m}^2/\text{s}
\]

### Result:
The angular momentum of the top is approximately \(0.00245 \, \text{kg m}^2/\text{s}\).

Would you like further details on this calculation or have any questions? Here are some related questions for your consideration:

1. How does the angle of lean affect the stability of the top?
2. What other factors can influence the angular momentum of a spinning object?
3. How would the angular momentum change if the top were spinning faster?
4. What is the relationship between linear velocity and angular velocity?
5. Can you explain the concept of moment of inertia and its role in angular momentum? 

**Tip:** Remember that angular momentum is a vector quantity and has both magnitude and direction, which can change depending on the rotation axis.

Discover how to calculate the angular momentum of a 0.02-kg top spinning with a linear velocity of 2.41 m/s in a circle 10.2 cm wide, leaning at an angle of 87.7°. This problem utilizes the angular momentum formula, providing insights for high school physics students.

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