Math Problem Statement

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.

Solution

The formula shown in the image is calculating velocity vv using the equation:

v=πdw1n160000v = \frac{\pi \cdot d_{w1} \cdot n_1}{60000}

where:

  • dw1d_{w1} seems to represent a diameter (possibly of a wheel or a rotating object).
  • n1n_1 is likely the rotational speed in revolutions per minute (RPM).
  • 6000060000 is used to convert from RPM to a linear velocity (in meters per second).

In the example: v=π26.846145060000v = \frac{\pi \cdot 26.846 \cdot 1450}{60000}

This equals approximately: v2.038m/sv \approx 2.038 \, \text{m/s}

This result, 2.038m/s2.038 \, \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 dw1d_{w1} and n1n_1 in the given formula?
  2. How does multiplying by π\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 n1n_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.

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Math Problem Analysis

Mathematical Concepts

Circular Motion
Linear Velocity
Unit Conversion

Formulas

v = (π * d_w1 * n_1) / 60000

Theorems

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Suitable Grade Level

Grades 11-12