Moment of inertia given radius of gyration Calculator

✖The Area of Cross-Section is the enclosed surface area, product of length and breadth.ⓘ Area of Cross-Section [A]			+10% -10%
✖The Radius of Gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass.ⓘ Radius of Gyration [k_G]			+10% -10%

✖Rotational Inertia is a physical property of an object that quantifies its resistance to rotational motion about a particular axis.ⓘ Moment of inertia given radius of gyration [I_r]

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Moment of inertia given radius of gyration Solution

STEP 0: Pre-Calculation Summary

Formula Used

Rotational Inertia = Area of Cross-Section*Radius of Gyration^2
I_r = A*k_G^2
This formula uses 3 Variables

Variables Used

Rotational Inertia - (Measured in Meter⁴) - Rotational Inertia is a physical property of an object that quantifies its resistance to rotational motion about a particular axis.
Area of Cross-Section - (Measured in Square Meter) - The Area of Cross-Section is the enclosed surface area, product of length and breadth.
Radius of Gyration - (Measured in Meter) - The Radius of Gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass.

STEP 1: Convert Input(s) to Base Unit

Area of Cross-Section: 50 Square Meter --> 50 Square Meter No Conversion Required
Radius of Gyration: 4.43 Meter --> 4.43 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

I_r = A*k_G^2 --> 50*4.43^2

Evaluating ... ...

I_r = 981.245

STEP 3: Convert Result to Output's Unit

981.245 Meter⁴ --> No Conversion Required

FINAL ANSWER

981.245 Meter⁴ <-- Rotational Inertia

(Calculation completed in 00.004 seconds)

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< Mechanics and Statistics of Materials Calculators

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Radius of gyration given moment of inertia and area

LaTeX Go Radius of Gyration = sqrt(Rotational Inertia/Area of Cross-Section)

Moment of inertia given radius of gyration

LaTeX Go Rotational Inertia = Area of Cross-Section*Radius of Gyration^2

Moment of inertia of circle about diametrical axis

LaTeX Go Rotational Inertia = (pi*Diameter of Circle^4)/64

Moment of inertia given radius of gyration Formula

LaTeX Go

Rotational Inertia = Area of Cross-Section*Radius of Gyration^2
I_r = A*k_G^2

What is moment of inertia?

Moment of inertia is defined as the quantity expressed by the body resisting angular acceleration which is the sum of the product of the mass of every particle with its square of a distance from the axis of rotation.

How to Calculate Moment of inertia given radius of gyration?

Moment of inertia given radius of gyration calculator uses Rotational Inertia = Area of Cross-Section*Radius of Gyration^2 to calculate the Rotational Inertia, The Moment of inertia given radius of gyration formula is defined as the product of the area of cross-section and the square of the radius of gyration. Rotational Inertia is denoted by I_r symbol.

How to calculate Moment of inertia given radius of gyration using this online calculator? To use this online calculator for Moment of inertia given radius of gyration, enter Area of Cross-Section (A) & Radius of Gyration (k_G) and hit the calculate button. Here is how the Moment of inertia given radius of gyration calculation can be explained with given input values -> 981.245 = 50*4.43^2.

FAQ

What is Moment of inertia given radius of gyration?

The Moment of inertia given radius of gyration formula is defined as the product of the area of cross-section and the square of the radius of gyration and is represented as I_r = A*k_G^2 or Rotational Inertia = Area of Cross-Section*Radius of Gyration^2. The Area of Cross-Section is the enclosed surface area, product of length and breadth & The Radius of Gyration or gyradius is defined as the radial distance to a point that would have a moment of inertia the same as the body's actual distribution of mass.

How to calculate Moment of inertia given radius of gyration?

The Moment of inertia given radius of gyration formula is defined as the product of the area of cross-section and the square of the radius of gyration is calculated using Rotational Inertia = Area of Cross-Section*Radius of Gyration^2. To calculate Moment of inertia given radius of gyration, you need Area of Cross-Section (A) & Radius of Gyration (k_G). With our tool, you need to enter the respective value for Area of Cross-Section & Radius of Gyration and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Rotational Inertia?

In this formula, Rotational Inertia uses Area of Cross-Section & Radius of Gyration. We can use 1 other way(s) to calculate the same, which is/are as follows -

Rotational Inertia = (pi*Diameter of Circle^4)/64

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