https://file.aiquickdraw.com/mathbot/file/1729753631278slid1w3o.jpg

The formula shown in the image is calculating velocity \( v \) using the equation:

\[
v = \frac{\pi \cdot d_{w1} \cdot n_1}{60000}
\]

where:
- \( d_{w1} \) seems to represent a diameter (possibly of a wheel or a rotating object).
- \( n_1 \) is likely the rotational speed in revolutions per minute (RPM).
- \( 60000 \) is used to convert from RPM to a linear velocity (in meters per second).

In the example:
\[
v = \frac{\pi \cdot 26.846 \cdot 1450}{60000}
\]

This equals approximately:
\[
v \approx 2.038 \, \text{m/s}
\]

This result, \( 2.038 \, \text{m/s} \), is the calculated velocity.

Would you like more details or have any further questions?

Here are 5 related questions to consider:
1. What are the units of \( d_{w1} \) and \( n_1 \) in the given formula?
2. How does multiplying by \( \pi \) affect the relationship between rotational speed and velocity?
3. What physical scenario might this formula describe (e.g., wheel on a vehicle)?
4. Why is the number 60000 used to convert units in this formula?
5. What adjustments would be needed if \( n_1 \) were in radians per second instead of RPM?

**Tip:** Always ensure unit consistency when applying formulas, especially when converting between angular and linear velocities.

The image shows a calculation of velocity using the equation: v = (π * d_w1 * n_1) / 60000, with specific values substituted for d_w1 and n_1.

Learn how to calculate velocity from rotational speed (RPM) and diameter using the formula v = (π * d_w1 * n_1) / 60000. This example involves unit conversion and the application of circular motion principles, making it suitable for students in Grades 11-12.

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