Ferris Wheel Equation Calculator

The Ferris Wheel Equation Calculator helps you calculate the position of a point on a Ferris wheel at a given time. This is especially useful for understanding circular motion and its related dynamics, including angular velocity and trigonometric relationships.

Calculation Overview

The motion of a Ferris wheel follows circular dynamics. The position of a point on the wheel after a time \( t \) is given by the parametric equations:

\[ x = r \cdot \cos(\theta) \] \[ y = r \cdot \sin(\theta) \]

Where:

• \( r \) is the radius of the Ferris wheel,
• \( \theta \) is the angular displacement in radians, which is calculated as \( \theta = \omega \cdot t \) (with \( \omega \) as the angular velocity in radians per second).

\[ \omega = \frac{2 \pi \cdot \text{RPM}}{60} \]

Example Calculation

If a Ferris wheel has a radius of 20 meters and rotates at 5 RPM, and you want to calculate the position after 30 seconds, the calculator will find the angular displacement and give the corresponding coordinates.