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Institute of Aeronautical Engineering (IARE), Hyderabad
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Moment of inertia given radius of gyration Solution

STEP 0: Pre-Calculation Summary
Formula Used
area_momentofinertia = Area of cross section*Radius of gyration^2
I = A*kG^2
This formula uses 2 Variables
Variables Used
Area of cross section - Area of cross section is the enclosed surface area, product of length and breadth. (Measured in Square Meter)
Radius of gyration - Radius of gyration or gyradius of a body about an axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concentrated there. (Measured in Meter)
STEP 1: Convert Input(s) to Base Unit
Area of cross section: 48 Square Meter --> 48 Square Meter No Conversion Required
Radius of gyration: 3 Meter --> 3 Meter No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
I = A*kG^2 --> 48*3^2
Evaluating ... ...
I = 432
STEP 3: Convert Result to Output's Unit
432 Meter⁴ --> No Conversion Required
FINAL ANSWER
432 Meter⁴ <-- Area Moment Of Inertia
(Calculation completed in 00.009 seconds)

3 Properties of surfaces and solids Calculators

Radius of gyration given moment of inertia and area
radius_of_gyration = sqrt(Area Moment Of Inertia/Area of cross section) Go
Moment of inertia given radius of gyration
area_momentofinertia = Area of cross section*Radius of gyration^2 Go
Moment of inertia of circle about diametrical axis
area_momentofinertia = (pi*Diameter^4)/64 Go

Moment of inertia given radius of gyration Formula

area_momentofinertia = Area of cross section*Radius of gyration^2
I = A*kG^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 area_momentofinertia = Area of cross section*Radius of gyration^2 to calculate the Area Moment Of Inertia, The Moment of inertia given radius of gyration formula is defined as the product of area of cross section and square of radius of gyration. Area Moment Of Inertia and is denoted by I 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) and Radius of gyration (kG) and hit the calculate button. Here is how the Moment of inertia given radius of gyration calculation can be explained with given input values -> 432 = 48*3^2.

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 area of cross section and square of radius of gyration and is represented as I = A*kG^2 or area_momentofinertia = Area of cross section*Radius of gyration^2. Area of cross section is the enclosed surface area, product of length and breadth and Radius of gyration or gyradius of a body about an axis of rotation is defined as the radial distance to a point which would have a moment of inertia the same as the body's actual distribution of mass, if the total mass of the body were concentrated there.
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 area of cross section and square of radius of gyration is calculated using area_momentofinertia = Area of cross section*Radius of gyration^2. To calculate Moment of inertia given radius of gyration, you need Area of cross section (A) and Radius of gyration (kG). With our tool, you need to enter the respective value for Area of cross section and 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 Area Moment Of Inertia?
In this formula, Area Moment Of Inertia uses Area of cross section and Radius of gyration. We can use 3 other way(s) to calculate the same, which is/are as follows -
  • radius_of_gyration = sqrt(Area Moment Of Inertia/Area of cross section)
  • area_momentofinertia = Area of cross section*Radius of gyration^2
  • area_momentofinertia = (pi*Diameter^4)/64
Where is the Moment of inertia given radius of gyration calculator used?
Among many, Moment of inertia given radius of gyration calculator is widely used in real life applications like {FormulaUses}. Here are few more real life examples -
{FormulaExamplesList}
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