Average Circular Velocity

Radius (\( R \)):

Lap Time (\( T \)):

Velocity (\( v \)) in meters/second (m/s):

Velocity (\( v \)) in feet/second (ft/s):

Velocity (\( v \)) in meters/minute (m/min):

Velocity (\( v \)) in feet/minute (ft/min):

Velocity (\( v \)) in miles/hour (mph):

Velocity (\( v \)) in kilometers/hour (km/h):

1. What is the Linear Velocity Calculator?

Definition: This calculator determines the linear velocity (\( v \)) of an object moving in a circular path based on its radius (\( R \)) and lap time (\( T \)).

Purpose: It assists physicists and engineers in analyzing the speed of rotating or circular motion systems.

2. How Does the Calculator Work?

The calculator uses the relationship:

\[ v = \frac{2 \cdot \pi \cdot R}{T} \]

Where:

\( v \) — Linear velocity (in various units)
\( R \) — Radius of the circular path
\( T \) — Lap time (time for one complete revolution)

Explanation: Enter the radius and lap time in the chosen units, and the calculator computes the linear velocity in multiple units. Results use scientific notation (5 decimal places) if the velocity in meters/second is greater than 1000 or less than 0.00001, otherwise 2 decimal places. The image output (4.8224628282473 m/s for \( R = 25.52 \, \text{m} \), \( T = 33.25 \, \text{s} \)) matches the calculation.

3. Importance of Linear Velocity

Details: Linear velocity is essential for understanding the speed of objects in circular motion, used in designing systems like wheels, gears, and planetary motion.

4. Using the Calculator

Tips: Enter positive values for radius and lap time, then click "Calculate." Results show linear velocity in various units (scientific notation with 5 decimal places if > 1000 or < 0.00001 m/s, otherwise 2 decimal places).

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