1. What is Cylindrical Coordinate System?

The cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the angle from a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis.

2. How Does the Calculator Work?

The calculator converts Cartesian coordinates (x, y, z) to cylindrical coordinates (r, θ, z):

Where:

• \( r \) — Radial distance from the z-axis
• \( \theta \) — Azimuthal angle in the x-y plane from the x-axis
• \( z \) — Height above the x-y plane (same as Cartesian z)

Explanation: The calculator takes Cartesian coordinates and converts them to the equivalent cylindrical coordinate representation.

3. Applications of Cylindrical Coordinates

Details: Cylindrical coordinates are commonly used in physics and engineering, especially in problems with cylindrical symmetry like fluid flow in pipes, electromagnetic fields around wires, and heat transfer in cylindrical objects.

4. Using the Calculator

Tips: Enter the Cartesian x, y, and z coordinates. The calculator will compute the equivalent cylindrical coordinates (r, θ, z). Angle θ is provided in both radians and degrees.

5. Frequently Asked Questions (FAQ)

Q1: What's the difference between cylindrical and spherical coordinates?
A: Cylindrical coordinates use a radial distance, angle, and height (r, θ, z), while spherical coordinates use radial distance and two angles (r, θ, φ).

Q2: How is θ angle measured?
A: θ is measured from the positive x-axis in the x-y plane, with positive values counterclockwise.

Q3: What's the range of θ values?
A: Typically -π to π radians (-180° to 180°), but sometimes 0 to 2π radians (0° to 360°).

Q4: Can r be negative?
A: No, r is always non-negative as it represents a distance.

Q5: When are cylindrical coordinates preferred over Cartesian?
A: When the problem has cylindrical symmetry, as equations often simplify in cylindrical coordinates.