Radius of gyration given moment of inertia and area Calculator

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Moment of Inertia in Solids

✖Rotational Inertia is a physical property of an object that quantifies its resistance to rotational motion about a particular axis.ⓘ Rotational Inertia [I_r]			+10% -10%
✖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 given moment of inertia and area [k_G]

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Radius of gyration given moment of inertia and area

Formula

`"k"_{"G"} = sqrt("I"_{"r"}/"A")`

Example

`"4.429447m"=sqrt("981m⁴"/"50m²")`

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Radius of gyration given moment of inertia and area Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius of Gyration = sqrt(Rotational Inertia/Area of Cross-Section)
k_G = sqrt(I_r/A)
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

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.
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.

STEP 1: Convert Input(s) to Base Unit

Rotational Inertia: 981 Meter⁴ --> 981 Meter⁴ No Conversion Required
Area of Cross-Section: 50 Square Meter --> 50 Square Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

k_G = sqrt(I_r/A) --> sqrt(981/50)

Evaluating ... ...

k_G = 4.42944691807002

STEP 3: Convert Result to Output's Unit

4.42944691807002 Meter --> No Conversion Required

FINAL ANSWER

4.42944691807002 ≈ 4.429447 Meter <-- Radius of Gyration

(Calculation completed in 00.004 seconds)

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< 14 Mechanics and Statistics of Materials Calculators

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Go Inclination of Resultant forces = atan((Second Force*sin(Angle))/(First Force+Second Force*cos(Angle)))

Resultant of Two Forces acting on Particle with Angle

Go Parallel Resultant Force = sqrt(First Force^2+2*First Force*Second Force*cos(Angle)+Second Force^2)

Radius of gyration given moment of inertia and area

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

Resolution of Force with Angle along Horizontal Direction

Go Horizontal Component of Force = Force at Angle*cos(Angle)

Resolution of Force with Angle along Vertical Direction

Go Vertical component of force = Force at Angle*sin(Angle)

Resultant of Two Forces Acting on Particle at 90 Degrees

Go Resultant force = sqrt(First Force^2+Second Force^2)

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Go Moment of force = Force*Perpendicular Distance between Force and Point

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Go Moment of Couple = Force*Perpendicular Distance between Two Forces

Moment of inertia given radius of gyration

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

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Go Parallel Resultant Force = First Force+Second Force

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

Resultant of Two like Parallel Forces

Go Parallel Resultant Force = First Force+Second Force

Resultant of Two Unlike Parallel Forces Unequal in Magnitude

Go Resultant force = First Force-Second Force

Resultant of Two Forces Acting on Particle at 180 Degrees

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Radius of gyration given moment of inertia and area Formula

Radius of Gyration = sqrt(Rotational Inertia/Area of Cross-Section)
k_G = sqrt(I_r/A)

What is radius of gyration?

Radius of gyration is the distance from an axis at which the mass of a body may be assumed to be concentrated and at which the moment of inertia will be equal to the moment of inertia of the actual mass about the axis.

How to Calculate Radius of gyration given moment of inertia and area?

Radius of gyration given moment of inertia and area calculator uses Radius of Gyration = sqrt(Rotational Inertia/Area of Cross-Section) to calculate the Radius of Gyration, The Radius of gyration given moment of inertia and area formula is defined as the square root of ratio of moment of inertia to area. Radius of Gyration is denoted by k_G symbol.

How to calculate Radius of gyration given moment of inertia and area using this online calculator? To use this online calculator for Radius of gyration given moment of inertia and area, enter Rotational Inertia (I_r) & Area of Cross-Section (A) and hit the calculate button. Here is how the Radius of gyration given moment of inertia and area calculation can be explained with given input values -> 0.43589 = sqrt(981/50).

FAQ

What is Radius of gyration given moment of inertia and area?

The Radius of gyration given moment of inertia and area formula is defined as the square root of ratio of moment of inertia to area and is represented as k_G = sqrt(I_r/A) or Radius of Gyration = sqrt(Rotational Inertia/Area of Cross-Section). Rotational Inertia is a physical property of an object that quantifies its resistance to rotational motion about a particular axis & The Area of Cross-Section is the enclosed surface area, product of length and breadth.

How to calculate Radius of gyration given moment of inertia and area?

The Radius of gyration given moment of inertia and area formula is defined as the square root of ratio of moment of inertia to area is calculated using Radius of Gyration = sqrt(Rotational Inertia/Area of Cross-Section). To calculate Radius of gyration given moment of inertia and area, you need Rotational Inertia (I_r) & Area of Cross-Section (A). With our tool, you need to enter the respective value for Rotational Inertia & Area of Cross-Section and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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