Enter the moment of inertia and mass into the calculator to determine the radius of gyration.
Radius of Gyration Calculation Formula
The following formula is used to calculate the radius of gyration:
$$k = \sqrt{\frac{I}{m}}$$
Variables:
- \( k \) is the radius of gyration (m)
- \( I \) is the moment of inertia (kg·m²)
- \( m \) is the mass (kg)
To calculate the radius of gyration, divide the moment of inertia by the mass and take the square root of the result.
What is Radius of Gyration?
The radius of gyration is a measure of the distribution of the mass of an object around an axis of rotation. It represents the distance from the axis at which the mass of the body could be concentrated without altering its rotational inertia. This concept is crucial in structural engineering and mechanics, as it helps to determine the buckling strength of columns and the dynamic behavior of rotating objects.
How to Calculate Radius of Gyration?
The following steps outline how to calculate the radius of gyration using the given formula.
- First, determine the moment of inertia (\(I\)) of the object. This can be found through experiments or standard tables for common shapes.
- Next, determine the mass (\(m\)) of the object.
- Use the formula: \( k = \sqrt{\frac{I}{m}} \).
- Finally, calculate the radius of gyration by plugging in the values for \( I \) and \( m \).
- After inserting the variables and calculating the result, verify your answer using the calculator above.
Example Problem:
Use the following variables