Cylinder (Solid) - Radius of Gyration about y-axis

Radius of Gyration (\( r_{yc} = r_y \)) in meters (m):

Radius of Gyration (\( r_{yc} = r_y \)) in centimeters (cm):

Radius of Gyration (\( r_{yc} = r_y \)) in feet (ft):

Radius of Gyration (\( r_{yc} = r_y \)) in inches (in):

1. What is the Radius of Gyration Calculator?

Definition: This calculator computes the radius of gyration (\( r_{yc} = r_y \)) of a solid cylinder about the y-axis (along the cylinder's height), based on its radius (\( R \)).

Purpose: It is used in mechanics and engineering to analyze the mass distribution of a rotating cylinder, applicable in designs involving rotating machinery, structural beams, and dynamics studies.

2. How Does the Calculator Work?

The calculator uses the relationship:

\[ r_{yc} = r_y = \frac{R}{\sqrt{2}} \]

Where:

\( r_{yc} = r_y \) — Radius of gyration about the y-axis (in various units)
\( R \) — Radius of the cylinder's base

Explanation: Enter the radius of the cylinder in the chosen units, and the calculator computes the radius of gyration. Results are displayed with 5 decimal places. For the default input (\( R = 0.1 \, \text{m} \)), the calculated radius of gyration \( r_{yc} = r_y \) is approximately 0.07071 m.

3. Importance of the Radius of Gyration

Details: The radius of gyration represents the distribution of an object's mass relative to an axis of rotation. It is crucial for calculating the moment of inertia (\( I = m \cdot r^2 \)) and understanding rotational dynamics in engineering applications.

4. Using the Calculator

Tips: Enter a positive value for the radius with up to 4 decimal places (step of 0.0001), then click "Calculate." Results show the radius of gyration \( r_{yc} = r_y \) in meters, centimeters, feet, and inches, always with 5 decimal places.

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