# Rotational Stiffness Calculator

Created by Rahul Dhari
Reviewed by Steven Wooding
Last updated: Jan 18, 2024

The rotational stiffness calculator determines a body's rotational stiffness using the angle of rotation and the applied momentum. The rotational stiffness is important to study to assess an object's ability to deform under loading conditions. The application of the concept can be found in different studies involving turbines, vibrations, and springs. Read on to understand the rotational stiffness formula and how to calculate rotational stiffness.

## Rotational stiffness

Before explaining rotational stiffness, let's take a look at stiffness. The stiffness is a property of a body that is defined as the resistance to deformation under loads. The stiffness of a body $k$ can be written as the ratio of force applied $F$ to the displacement $\delta$ produced due to the force as:

$k = \frac{F}{\delta}$

🙋 Yup, you are not wrong, this definition is fairly similar to the one we explored in our Young's modulus calculator!

Similarly, the rotational stiffness is defined as the property of a body to resist rotation or the ratio of applied momentum $M$ to the angle of rotation $\Theta$. Mathematically, the rotational stiffness equation can be written as:

$k = \frac{M}{\Theta}$

🙋 For a refresh on the concept mentioned above, visit our momentum calculator and our displacement calculator.

## How to find rotational stiffness?

Follow the steps below to calculate the rotational stiffness of a body, using this calculator:

• Step 1: Enter the value of applied momentum.
• Step 2: Insert the value of rotation angle in radians.
• Step 3: The calculator will now return the value of rotational stiffness.

## Using the rotational stiffness calculator

Find the rotational stiffness of an object rotated to an angle of $0.7$ radians, having applied momentum of $16\ \mathrm{N\cdot m}$.

• Step 1: Enter the value of applied momentum, $M =16\ \mathrm{N\cdot m}$.
• Step 2: Insert the value of rotation angle in radians, $\Theta = 0.7$ radians.
• Step 3: The calculator will now use the rotational stiffness equation:
$k = \frac{M}{\Theta} = \frac{16}{0.7} = 22.857\ \mathrm{N\cdot m/rad}$

Therefore, to deform the object, it would take $22.857\ \mathrm{N\cdot m}$ of momentum per every radian of rotation.

## Applications of rotational stiffness

Did you know?

• Rotational stiffness is used in foundations and construction work. The rotational stiffness formula is used to estimate the stiffness of a circular foundation subjected to rocking motion.
• Rotational stiffness is also significant in building construction, to calculate the rigidity of individual structural elements, beams, columns, arches.
• The parameter is also associated with mechanical components such as wings of an aircraft, and building and construction components as chimneys, where crossflow winds can induce vibrations.
• The design and construction of offshore wind turbine platforms also takes rotational stiffness into account to design for maximum stability whilst it floats in the ocean among different intensities of water waves.

🙋 You are not looking for the rotational stiffness? Maybe you are looking for the torsional stiffness calculator! 😉

## FAQ

### What is stiffness?

The stiffness is a property of a body to resist deforming under loads. Mathematically, stiffness is the ratio of force applied to displacement.

### What is rotational stiffness?

Rotational stiffness is defined as ratio of the applied momentum to the angle of rotation. In other words, the amount of applied momentum required per radian of rotation.

### What are units of rotational stiffness?

Rotational stiffness is measured in kiloNewton meter per radian (kN · m/rad) or kiloNewton meter per degree Nmº.

### How do I calculate rotational stiffness?

To calculate rotational stiffness: Divide the applied momentum by the angle of rotation.

Rahul Dhari
Applied moment
lbf·ft
Angle of rotation
Rotational stiffness
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